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Bosnia and Herzegovina TST 2000 Day 1 Problem 3

Source: Bosnia and Herzegovina Team Selection Test 2000

September 19, 2018

Pythagorean Triplenumber theory

Problem Statement

We call Pythagorean triple a triple

(x,y,z)

of positive integers such that

x<y<z

and

x^2+y^2=z^2

. Prove that for all

n \in \mathbb{N}

number

2^{n+1}

is in exactly

n

Pythagorean triples