%hw4.tex: Homework assignment 4
%%a Plain TeX file by Doron Zeilberger

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\centerline
{
\bf Dr. Z.'s Number Theory Homework assignment 4
}


{\bf 1.} Convert the following to binary, in (i) sparse notation (ii) dense notation (iii) positional notation.

{\bf a.} $17$ \quad {\bf b.}  $257$ \quad {\bf c.}  $515$ \quad .



{\bf 2.} Convert the following to base $5$, in (i) sparse notation (ii) dense notation (iii) positional notation.

{\bf a.} $130$ \quad {\bf b.}  $631$ 


{\bf 3.} Find, in base $6$, 
$$
(5 \cdot 6^3 +  1 \cdot 6^0)+
(4 \cdot 6^3 +  5 \cdot 6^1 +  5 \cdot 6^0)
$$


{\bf 4.} Find, in base $6$, 
$$
(5 \cdot 6^3 +  1 \cdot 6^0) \cdot
(4 \cdot 6^3 +  5 \cdot 6^1 +  5 \cdot 6^0) \quad .
$$

{\bf 5.} Use Karatsuba's algorithm (no credit for other methods!), to find
the product
$$
87 \cdot 93 \quad .
$$

\end
