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4

Part of 2016 China Second Round Olympiad

Problems(1)

nice problem

Source: China Second Round Olympiad 2016 Test 2 Q4

9/12/2016
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
Sequencenumber theoryChina second round