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Diophantine with polynomial and exponential

Source: 2020 1st OMpD L3 P1 - Brazil - Olimpíada Matemáticos por Diversão

July 8, 2023
number theoryDiophantine equationExponential equationpolynomialalgebra

Problem Statement

Determine all pairs of positive integers (x,y)(x, y) such that: x4−6x2+1=7⋅2yx^4 - 6x^2 + 1 = 7\cdot 2^y
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