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SAQ: P 5

Part of 2018 Mathematical Talent Reward Programme

Problems(1)

Prove these two problems on Fibonacci sequence.

Source: MTRP 2018 Class 11-Short Answer Type Question: Problem 5 :-

2/17/2021
[*] Prove that, the sequence of remainders obtained when the Fibonacci numbers are divided by nn is periodic, where nn is a natural number. [*] There exists no such non-constant polynomial with integer coefficients such that for every Fibonacci number n,n, P(n) P(n) is a prime.
Fibonacci sequenceremainderPeriodic sequencepolynomialalgebra