MathDB

BP3

Part of 2020 China Northern MO

Problems(1)

19 divides 1+2^n+3^n+4^n

Source: 2020 China North Mathematical Olympiad Basic Level P3

8/4/2020
Are there infinitely many positive integers nn such that 19∣1+2n+3n+4n19|1+2^n+3^n+4^n? Justify your claim.
number theoryDivisibilityExistence