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4

Part of 2011 Turkey MO (2nd round)

Problems(1)

Turkey NMO 2011 Problem 4

Source:

12/10/2011
a1=5a_{1}=5 and an+1=an3−2an2+2a_{n+1}=a_{n}^{3}-2a_{n}^{2}+2 for all n≥1n\geq1. pp is a prime such that p=3(mod4)p=3(mod 4) and p∣a2011+1p|a_{2011}+1. Show that p=3p=3.
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