MathDB
Weird sequence NT

Source: 239 MO 2024 S7

May 22, 2024
number theory

Problem Statement

Let n>3n>3 be a positive integer satisfying 2n+1=3p2^n+1=3p, where pp is a prime. Let s0=2n−2+13s_0=\frac{2^{n-2}+1}{3} and si=si−12−2s_i=s_{i-1}^2-2 for i>0i>0. Show that p∣2sn−2−3p \mid 2s_{n-2}-3.
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