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Number of solutions to 3^x-2^y.

Source: ISR 2021 TST1 p.4

May 4, 2022
Diophantine equationnumber theory

Problem Statement

Let rr be a positive integer and let ara_r be the number of solutions to the equation 3x−2y=r3^x-2^y=r ,such that 0≤x,y≤57810\leq x,y\leq 5781 are integers. What is the maximal value of ara_r?
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