$3^m+7^n$ is a perfect square!!

Asked May 12 '19 at 15:50

Active May 12 '19 at 15:52

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Determine all pairs $(m,n)$ of positive integers such that $3^m+7^n$ is a perfect square

when n and m are both odd $3^m+7^n$ isn't a perfect square. and when n and m are both even $3^m+7^n$ isn't a perfect square. But I can't figure out the other cases.

Can someone helps me!

edited May 12 '19 at 15:52

MachineLearner

3,991

asked May 12 '19 at 15:50

Nadun Rajapaksha

2

Isn't $$16=7^1+3^2$$? – Dr. Sonnhard Graubner May 12 '19 at 15:52
The solution in the previous comment is the only one with $m,n\leq250$ – saulspatz May 12 '19 at 16:01

$3^m+7^n$ is a perfect square!!

0 Answers0