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2^n = 7x^2 + y^2 , diophantine

Source: 1997 Estonia National Olympiad Final Round grade 9 p1

March 13, 2020

number theorydiophantineDiophantine equation

Problem Statement

Prove that for every integer

n\ge 3

there are such positives integers

x

and

y

such that

2^n = 7x^2 + y^2