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Source: China Second Round Olympiad 2016 Test 2 Q4

September 12, 2016
Sequencenumber theoryChina second round

Problem Statement

Let p>3p>3 and p+2p+2 are prime numbers,and define sequence a1=2,an=an−1+⌊pan−1n⌋a_{1}=2,a_{n}=a_{n-1}+\lfloor \dfrac{pa_{n-1}}{n}\rfloor
show that:for any n=3,4,⋯ ,p−1n=3,4,\cdots,p-1 have n∣pan−1+1n|pa_{n-1}+1
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