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Found problems: 26

2018 Mathematical Talent Reward Programme, SAQ: P 5
Tags: fibonacci sequence , remainder , periodic sequence , polynomial , algebra
[list=1] [*] Prove that, the sequence of remainders obtained when the Fibonacci numbers are divided by $n$ is periodic, where $n$ is a natural number. [*] There exists no such non-constant polynomial with integer coefficients such that for every Fibonacci number $n,$ $ P(n)$ is a prime. [/list]