1

Part of 1997 Abels Math Contest (Norwegian MO)

Problems(1)

happy naturals , a^2+b^2 = n, sum of perfect squares

Source: Norwegian Mathematical Olympiad 1997 - Abel Competition p1

We call a positive integer

n

happy if there exist integers

a,b

a^2+b^2 = n

t

is happy, show that (a)

2t

3t

Perfect SquareSumnumber theory