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3^x + 7^y a perfect squatre

Source: Norwegian Mathematical Olympiad 2015 - Abel Competition p4

September 3, 2019

number theoryexponentialPerfect Square

Problem Statement

a. Determine all nonnegative integers

x

and

y

so that

3^x + 7^y

is a perfect square and

y

is even. b. Determine all nonnegative integers

x

and

y

so that

3^x + 7^y

is a perfect square and

y

is odd