MathDB

1

Part of 2023 IRN-SGP-TWN Friendly Math Competition

Problems(1)

A familiar NT construction

Source: 2023 IRN-SGP-TWN Friendly Math Competition P1

7/16/2023
Prove that there are infinitely many positive integers aa such that a!+(a+2)!∣(a+2⌊a⌋)!.a!+(a+2)!\mid (a+2\left\lfloor\sqrt{a}\right\rfloor)!.
Proposed by Navid and the4seasons.
number theory