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(a^2- 9b^2)^2 - 33b = 1 diophantine

Source: 2009 Romania District VIII p4

August 16, 2024
number theoryDiophantine equation

Problem Statement

Positive integer numbers a and b satisfy (a2−9b2)2−33b=1(a^2- 9b^2)^2 - 33b = 1. a) Prove ∣a−3b∣≥1|a -3b|\ge 1. b) Find all pairs of positive integers (a,b)(a, b) satisfying the equality.
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