%hw12.tex: Homework assignment 12
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\centerline
{
\bf Dr. Z.'s Number Theory Homework assignment 12
}

{\bf 1.} Using divisiblity tests, determine
which of the following 
integers (written in the usual, base $10$, way)
is divisible by (i) $9$ (ii)$11$ (iii)$7$.

{\bf a.} $6844430439$

{\bf b.} $178888708386$

{\bf c.} $1391356620$


{\bf 2.} Using divisiblity tests determine
which of the following 
integers are divisible by $99$ (i.e. by {\bf both}
$9$ and $11$)

{\bf a.} $976865076$

{\bf b.} $976865076$

{\bf c.} $171928253381$


{\bf 3.} Using divisiblity tests determine
which of the following 
integers, written in base $7$ 
are divisible (i) by $6$ (ii) $11$ (base $7$) 
(alias $8$ base $10$)

{\bf a.} $316653313$

{\bf b.} $35145$

{\bf c.}  $610040033223$

{\bf 4.} Using the Perpetual calendar algorithm, find out
on what day of the week 

       (i) were you born?

       (ii) you will turn 60-years-old

       (iii) turn 200-years-old



{\bf 5.} Using the Perpetual calendar algorithm, find out
on what day of the week 

       (i) was you mother born?

       (ii) was your father born?

       (iii) for each brother and sister find out the
             day of the week that they were born.
\end
