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

Source: 2020 China North Mathematical Olympiad Basic Level P3

August 4, 2020
number theoryDivisibilityExistence

Problem Statement

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