Competition problem — Number theory

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Number theory Difficulty 5.5 AIME, harder Find the answer

2. Find the first ten terms of the sequence of pseudo-random numbers generated by the linear congruential method with $x_{0}=6$ and $x_{n+1} \equiv 5 x_{n}+2(\bmod 19)$ . What is the period length of this generator?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

2. $6.13,10,14,15,1,7,18,16,6,13, \ldots$ period length is 9

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.