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%%a Plain TeX file by Shalosh B. Ekhad and Doron Zeilberger (x pages)

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\centerline
{\bf Anomalous Cancellation }
\bigskip
\centerline
{\it Shalosh B. EKHAD and Doron ZEILBERGER}






                                                                $\frac{\not64}{1\not60}=\frac{4}{10}$

                                                                $\frac{\not95}{1\not90}=\frac{5}{10}$

                                                                $\frac{\not96}{1\not92}=\frac{6}{12}$

                                                                $\frac{\not97}{1\not94}=\frac{7}{14}$

                                                               $\frac{2\not91}{1\not94}=\frac{21}{14}$

                                                                $\frac{\not98}{1\not96}=\frac{8}{16}$

                                                               $\frac{2\not94}{1\not96}=\frac{24}{16}$

                                                               $\frac{4\not90}{1\not96}=\frac{40}{16}$

                                                              $\frac{12\not21}{2\not22}=\frac{121}{22}$

                                                              $\frac{13\not42}{2\not44}=\frac{132}{24}$

                                                                $\frac{\not65}{2\not60}=\frac{5}{20}$

                                                               $\frac{6\not65}{2\not66}=\frac{65}{26}$

                                                              $\frac{14\not63}{2\not66}=\frac{143}{26}$

                                                              $\frac{22\not61}{2\not66}=\frac{221}{26}$

                                                              $\frac{15\not84}{2\not88}=\frac{154}{28}$

                                                                $\frac{\not97}{2\not91}=\frac{7}{21}$

                                                               $\frac{1\not94}{2\not91}=\frac{14}{21}$

                                                                $\frac{\not98}{2\not94}=\frac{8}{24}$

                                                               $\frac{1\not96}{2\not94}=\frac{16}{24}$

                                                               $\frac{3\not92}{2\not94}=\frac{32}{24}$

                                                               $\frac{4\not90}{2\not94}=\frac{40}{24}$

                                                               $\frac{8\not30}{3\not32}=\frac{80}{32}$

                                                               $\frac{1\not95}{3\not90}=\frac{15}{30}$

                                                                $\frac{\not98}{3\not92}=\frac{8}{32}$

                                                               $\frac{1\not96}{3\not92}=\frac{16}{32}$

                                                               $\frac{2\not94}{3\not92}=\frac{24}{32}$

                                                               $\frac{4\not90}{3\not92}=\frac{40}{32}$

                                                               $\frac{1\not97}{3\not94}=\frac{17}{34}$

                                                               $\frac{5\not91}{3\not94}=\frac{51}{34}$

                                                               $\frac{1\not99}{3\not98}=\frac{19}{38}$

                                                               $\frac{5\not97}{3\not98}=\frac{57}{38}$

                                                               $\frac{9\not95}{3\not98}=\frac{95}{38}$

                                                              $\frac{13\not93}{3\not98}=\frac{133}{38}$

                                                              $\frac{17\not91}{3\not98}=\frac{171}{38}$

                                                              $\frac{23\not21}{4\not22}=\frac{231}{42}$

                                                              $\frac{14\not43}{4\not44}=\frac{143}{44}$

                                                              $\frac{24\not42}{4\not44}=\frac{242}{44}$

                                                              $\frac{34\not41}{4\not44}=\frac{341}{44}$

                                                              $\frac{11\not60}{4\not64}=\frac{110}{44}$

                                                              $\frac{11\not65}{4\not66}=\frac{115}{46}$

                                                              $\frac{25\not63}{4\not66}=\frac{253}{46}$

                                                              $\frac{39\not61}{4\not66}=\frac{391}{46}$

                                                              $\frac{15\not86}{4\not88}=\frac{156}{48}$

                                                              $\frac{26\not84}{4\not88}=\frac{264}{48}$

                                                              $\frac{37\not82}{4\not88}=\frac{372}{48}$

                                                                $\frac{\not98}{4\not90}=\frac{8}{40}$

                                                               $\frac{1\not96}{4\not90}=\frac{16}{40}$

                                                               $\frac{2\not94}{4\not90}=\frac{24}{40}$

                                                               $\frac{3\not92}{4\not90}=\frac{32}{40}$

                                                               $\frac{1\not33}{5\not32}=\frac{13}{52}$

                                                               $\frac{9\not31}{5\not32}=\frac{91}{52}$

                                                              $\frac{13\not30}{5\not32}=\frac{130}{52}$

                                                              $\frac{15\not54}{5\not55}=\frac{154}{55}$

                                                              $\frac{25\not53}{5\not55}=\frac{253}{55}$

                                                              $\frac{35\not52}{5\not55}=\frac{352}{55}$

                                                              $\frac{45\not51}{5\not55}=\frac{451}{55}$

                                                              $\frac{18\not72}{5\not76}=\frac{182}{56}$

                                                               $\frac{2\not95}{5\not90}=\frac{25}{50}$

                                                               $\frac{1\not97}{5\not91}=\frac{17}{51}$

                                                               $\frac{3\not94}{5\not91}=\frac{34}{51}$

                                                               $\frac{2\not96}{5\not92}=\frac{26}{52}$

                                                               $\frac{2\not98}{5\not96}=\frac{28}{56}$

                                                               $\frac{8\not94}{5\not96}=\frac{84}{56}$

                                                              $\frac{14\not90}{5\not96}=\frac{140}{56}$

                                                               $\frac{1\not99}{5\not97}=\frac{19}{57}$

                                                               $\frac{3\not98}{5\not97}=\frac{38}{57}$

                                                               $\frac{7\not96}{5\not97}=\frac{76}{57}$

                                                               $\frac{9\not95}{5\not97}=\frac{95}{57}$

                                                              $\frac{13\not93}{5\not97}=\frac{133}{57}$

                                                              $\frac{15\not92}{5\not97}=\frac{152}{57}$

                                                              $\frac{19\not90}{5\not97}=\frac{190}{57}$

                                                               $\frac{2\not99}{5\not98}=\frac{29}{58}$

                                                               $\frac{8\not97}{5\not98}=\frac{87}{58}$

                                                              $\frac{14\not95}{5\not98}=\frac{145}{58}$

                                                              $\frac{20\not93}{5\not98}=\frac{203}{58}$

                                                              $\frac{26\not91}{5\not98}=\frac{261}{58}$

                                                              $\frac{34\not21}{6\not22}=\frac{341}{62}$

                                                              $\frac{35\not42}{6\not44}=\frac{352}{64}$

                                                               $\frac{1\not66}{6\not64}=\frac{16}{64}$

                                                              $\frac{11\not62}{6\not64}=\frac{112}{64}$

                                                              $\frac{16\not60}{6\not64}=\frac{160}{64}$

                                                               $\frac{2\not66}{6\not65}=\frac{26}{65}$

                                                              $\frac{10\not64}{6\not65}=\frac{104}{65}$

                                                              $\frac{14\not63}{6\not65}=\frac{143}{65}$

                                                              $\frac{18\not62}{6\not65}=\frac{182}{65}$

                                                              $\frac{22\not61}{6\not65}=\frac{221}{65}$

                                                              $\frac{16\not65}{6\not66}=\frac{165}{66}$

                                                              $\frac{36\not63}{6\not66}=\frac{363}{66}$

                                                              $\frac{56\not61}{6\not66}=\frac{561}{66}$

                                                              $\frac{37\not84}{6\not88}=\frac{374}{68}$

                                                              $\frac{18\not30}{7\not32}=\frac{180}{72}$

                                                              $\frac{21\not70}{7\not75}=\frac{210}{75}$

                                                              $\frac{17\not76}{7\not77}=\frac{176}{77}$

                                                              $\frac{27\not75}{7\not77}=\frac{275}{77}$

                                                              $\frac{37\not74}{7\not77}=\frac{374}{77}$

                                                              $\frac{47\not73}{7\not77}=\frac{473}{77}$

                                                              $\frac{57\not72}{7\not77}=\frac{572}{77}$

                                                              $\frac{67\not71}{7\not77}=\frac{671}{77}$

                                                               $\frac{3\not95}{7\not90}=\frac{35}{70}$

                                                               $\frac{3\not97}{7\not94}=\frac{37}{74}$

                                                              $\frac{11\not91}{7\not94}=\frac{111}{74}$

                                                               $\frac{1\not99}{7\not96}=\frac{19}{76}$

                                                               $\frac{3\not98}{7\not96}=\frac{38}{76}$

                                                               $\frac{5\not97}{7\not96}=\frac{57}{76}$

                                                               $\frac{9\not95}{7\not96}=\frac{95}{76}$

                                                              $\frac{11\not94}{7\not96}=\frac{114}{76}$

                                                              $\frac{13\not93}{7\not96}=\frac{133}{76}$

                                                              $\frac{17\not91}{7\not96}=\frac{171}{76}$

                                                              $\frac{19\not90}{7\not96}=\frac{190}{76}$

                                                               $\frac{3\not99}{7\not98}=\frac{39}{78}$

                                                              $\frac{11\not97}{7\not98}=\frac{117}{78}$

                                                              $\frac{19\not95}{7\not98}=\frac{195}{78}$

                                                              $\frac{27\not93}{7\not98}=\frac{273}{78}$

                                                              $\frac{35\not91}{7\not98}=\frac{351}{78}$

                                                              $\frac{45\not21}{8\not22}=\frac{451}{82}$

                                                               $\frac{3\not32}{8\not30}=\frac{32}{80}$

                                                              $\frac{27\not43}{8\not44}=\frac{273}{84}$

                                                              $\frac{46\not42}{8\not44}=\frac{462}{84}$

                                                              $\frac{65\not41}{8\not44}=\frac{651}{84}$

                                                              $\frac{19\not52}{8\not54}=\frac{192}{84}$

                                                              $\frac{30\not50}{8\not54}=\frac{300}{84}$

                                                              $\frac{21\not60}{8\not64}=\frac{210}{84}$

                                                              $\frac{21\not65}{8\not66}=\frac{215}{86}$

                                                              $\frac{47\not63}{8\not66}=\frac{473}{86}$

                                                              $\frac{73\not61}{8\not66}=\frac{731}{86}$

                                                              $\frac{18\not87}{8\not88}=\frac{187}{88}$

                                                              $\frac{28\not86}{8\not88}=\frac{286}{88}$

                                                              $\frac{38\not85}{8\not88}=\frac{385}{88}$

                                                              $\frac{48\not84}{8\not88}=\frac{484}{88}$

                                                              $\frac{58\not83}{8\not88}=\frac{583}{88}$

                                                              $\frac{68\not82}{8\not88}=\frac{682}{88}$

                                                              $\frac{78\not81}{8\not88}=\frac{781}{88}$

                                                               $\frac{2\not98}{8\not94}=\frac{28}{84}$

                                                               $\frac{5\not96}{8\not94}=\frac{56}{84}$

                                                              $\frac{11\not92}{8\not94}=\frac{112}{84}$

                                                              $\frac{14\not90}{8\not94}=\frac{140}{84}$

                                                               $\frac{2\not99}{8\not97}=\frac{29}{87}$

                                                               $\frac{5\not98}{8\not97}=\frac{58}{87}$

                                                              $\frac{11\not96}{8\not97}=\frac{116}{87}$

                                                              $\frac{14\not95}{8\not97}=\frac{145}{87}$

                                                              $\frac{20\not93}{8\not97}=\frac{203}{87}$

                                                              $\frac{23\not92}{8\not97}=\frac{232}{87}$

                                                              $\frac{29\not90}{8\not97}=\frac{290}{87}$

                                                               $\frac{1\not33}{9\not31}=\frac{13}{91}$

                                                               $\frac{5\not32}{9\not31}=\frac{52}{91}$

                                                              $\frac{13\not30}{9\not31}=\frac{130}{91}$

                                                               $\frac{2\not33}{9\not32}=\frac{23}{92}$

                                                              $\frac{16\not31}{9\not32}=\frac{161}{92}$

                                                              $\frac{23\not30}{9\not32}=\frac{230}{92}$

                                                              $\frac{20\not74}{9\not76}=\frac{204}{96}$

                                                              $\frac{31\not72}{9\not76}=\frac{312}{96}$

                                                              $\frac{42\not70}{9\not76}=\frac{420}{96}$

                                                               $\frac{4\not96}{9\not92}=\frac{46}{92}$

                                                               $\frac{4\not97}{9\not94}=\frac{47}{94}$

                                                              $\frac{14\not91}{9\not94}=\frac{141}{94}$

                                                               $\frac{1\not99}{9\not95}=\frac{19}{95}$

                                                               $\frac{3\not98}{9\not95}=\frac{38}{95}$

                                                               $\frac{5\not97}{9\not95}=\frac{57}{95}$

                                                               $\frac{7\not96}{9\not95}=\frac{76}{95}$

                                                              $\frac{11\not94}{9\not95}=\frac{114}{95}$

                                                              $\frac{13\not93}{9\not95}=\frac{133}{95}$

                                                              $\frac{15\not92}{9\not95}=\frac{152}{95}$

                                                              $\frac{17\not91}{9\not95}=\frac{171}{95}$

                                                               $\frac{4\not98}{9\not96}=\frac{48}{96}$

                                                              $\frac{14\not94}{9\not96}=\frac{144}{96}$

                                                              $\frac{24\not90}{9\not96}=\frac{240}{96}$

                                                               $\frac{4\not99}{9\not98}=\frac{49}{98}$

                                                              $\frac{14\not97}{9\not98}=\frac{147}{98}$

                                                              $\frac{24\not95}{9\not98}=\frac{245}{98}$

                                                              $\frac{34\not93}{9\not98}=\frac{343}{98}$

                                                              $\frac{44\not91}{9\not98}=\frac{441}{98}$



\bigskip
{\bf References}

\bigskip
\hrule
\bigskip
Shalosh B. Ekhad, c/o D. Zeilberger, Department of Mathematics, Rutgers University (New Brunswick), Hill Center-Busch Campus, 110 Frelinghuysen
Rd., Piscataway, NJ 08854-8019, USA. \hfill\break
Email: {\tt ShaloshBEkhad at gmail dot com}   \quad .
\bigskip
Doron Zeilberger, Department of Mathematics, Rutgers University (New Brunswick), Hill Center-Busch Campus, 110 Frelinghuysen
Rd., Piscataway, NJ 08854-8019, USA. \hfill\break
Email: {\tt DoronZeil at gmail  dot com}   \quad .


\end

