Competition problem — Number theory

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Number theory Difficulty 5.6 AIME, harder Find the answer

11. Find a good choice for the multiplier $a$ in the pure multiplicative pseudo-random number generator $x_{n} \equiv a x_{n-1}\left(\bmod 2^{25}-1\right)$ . (Hint: Find a primitive root of $2^{25}-1$ and then take an appropriate power of this root.)

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

None

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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.