A sequence x1,x2,...,xn,... consists of an initial block of p positive distinct integers that then repeat periodically. This means that {x1,x2,…,xp} are p distinct positive integers and xn+p=xn for every positive integer n. The terms of the sequence are not known and the goal is to find the period p. To do this, at each move it possible to reveal the value of a term of the sequence at your choice.(a) Knowing that 1≤p≤10, find the least n such that there is a strategy which allows to find p revealing at most n terms of the sequence.
(b) Knowing that p is one of the first k prime numbers, find for which values of k there exist a strategy that allows to find p revealing at most 5 terms of the sequence. number theoryprime numbers