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Primes in the form of 8k+1

Source: Junior Turkish Mathematical Olympiad 2011 P3

July 2, 2012
modular arithmeticnumber theory proposednumber theory

Problem Statement

m<nm < n are positive integers. Let p=n2+m2n2−m2p=\frac{n^2+m^2}{\sqrt{n^2-m^2}}.
(a) Find three pairs of positive integers (m,n)(m,n) that make pp prime.
(b) If pp is prime, then show that p≡1(mod8)p \equiv 1 \pmod 8.
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