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NT about sequence again

Source: 2022 China Second Round A2

December 22, 2022
number theorySequence and Series

Problem Statement

k>2k>2 is an integer. a0,a1,...a_0,a_1,... is an integer sequence such that a0=0a_0=0, an+1=kan−an−1a_{n+1}=ka_n-a_{n-1}. Prove that for any positive integer mm, (2m)!∣a1a2...a3m(2m)!|a_1a_2...a_{3m}.
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