CMO Senior Stage 2 Class 8 Homework
First name: ______________ Last name: _____________
Student ID: ______________
Number Theory 2
1. Find all pairs of positive integers x and y that satisfy 5 x − 7 y = 1 and x / y  2 .
2. Find all positive integers c, if any, such that the equation (m2 + 1)(n 2 + 1) = (cmn + 1)2 + 1 has
infinitely many positive integer solutions m, n.
3. Find five consecutive positive integers such that the first one is divisible by 5, the next one by 7,
the third by 9, the fourth by 11, and the fifth one by 13.
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CMO Senior Stage 2 Class 8 Homework
4. Find all positive integers n such that n2 + 25n + 19 is a perfect square.
5. For how many integers n is the quantity n2 − 20n + 244 equal to a perfect square?
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