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right triangle with sides a = p^m, b = q^n, hypotenuse c = 2k +1

Source: Dutch NMO 2004 p5

September 21, 2019

number theoryright triangle

Problem Statement

A right triangle with perpendicular sides

a

and

b

and hypotenuse

c

has the following properties:

a = p^m

and

b = q^n

with

p

and

q

prime numbers and

m

and

n

positive integers,

c = 2k +1

with

k

a positive integer. Determine all possible values of

c

and the associated values of

a

and

b