91Ó°ÊÓ

If \(a, x, y \in \mathbf{Z}\), and \(a \neq 0\), prove that \(a x=a y \Rightarrow x=y\)

Write a computer program (or develop an algorithm) to convert a positive integer in base 10 to base \(b\), where \(2 \leq b \leq 9\).

When does a positive integer \(n\) have exactly a) two positive divisors? b) three positive divisors? c) four positive divisors? d) five positive divisors?

a) For the five-digit integers (from 10000 to 99999 ) how many are palindromes and what is their sum? b) Write a computer program to check the answer for the sum in part (a).