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Diophantine equation involving factorials

Source: Mongolian Mathematical Olympiad 2024 P1

April 12, 2024
number theoryDiophantine equationfactorial

Problem Statement

Find all triples (a,b,c)(a, b, c) of positive integers such that a≤ba \leq b and a!+b!=c4+2024a!+b!=c^4+2024
Proposed by Otgonbayar Uuye.
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