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primes in a set of numbers

Source: 3rd National Women's Contest of Mexican Mathematics Olympiad 2024 , level 1+2 p8

June 14, 2024
primesnumber theory

Problem Statement

Find all positive integers nn such that among the nn numbers
2n+1, 22n+1, …, 2nn+1 2n + 1, \, 2^2 n + 1, \, \ldots, \, 2^n n + 1
there are nn, n−1n - 1, or n−2n - 2 primes.
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