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3^m + 3^n + k is perfect square for 0<=k<=9

Source: Norwegian Mathematical Olympiad 2021 - Abel Competition p3a

May 29, 2021
number theoryPerfect SquaresPerfect Square

Problem Statement

For which integers 0≤k≤90 \le k \le 9 do there exist positive integers mm and nn so that the number 3m+3n+k3^m + 3^n + k is a perfect square?
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