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every prime p divides floor(a+b*sqrt(2024)^p)-c

Source: CAPS 2024 p6

July 4, 2024
combinatoricsnumber theoryinternational competitionsCombinatorial Number Theoryprime numberstripletspositive integers

Problem Statement

Determine whether there exist infinitely many triples (a,b,c)(a, b, c) of positive integers such that every prime pp divides ⌊(a+b2024)p⌋−c.\left\lfloor\left(a+b\sqrt{2024}\right)^p\right\rfloor-c.
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