5

Part of 2004 Dutch Mathematical Olympiad

Problems(1)

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

Source: Dutch NMO 2004 p5

A right triangle with perpendicular sides

a

b

c

has the following properties:

a = p^m

b = q^n

p

q

prime numbers and

m

n

positive integers,

c = 2k +1

k

a positive integer. Determine all possible values of

c

and the associated values of

a

b

number theoryright triangle