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On x+3^y and y+3^x.

Source: Romanian District Olympiad 2022 - Grade 9 - Problem 3

March 27, 2022
number theoryDiophantine equationinduction

Problem Statement

a)a) Solve over the positive integers 3x=x+2.3^x=x+2. b)b) Find pairs (x,y)∈N×N(x,y)\in\mathbb{N}\times\mathbb{N} such that (x+3y)(x+3^y) and (y+3x)(y+3^x) are consecutive.
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