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a^{b + 20} (c-1) = c^{b + 21} - 1

Source: 2021 Austrian Federal Competition For Advanced Students, Part 2, p3

June 6, 2021
number theoryDiophantine equationdiophantine

Problem Statement

Find all triples (a,b,c)(a, b, c) of natural numbers a,ba, b and cc, for which ab+20(c−1)=cb+21−1a^{b + 20} (c-1) = c^{b + 21} - 1 is satisfied.
(Walther Janous)
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