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divisors on the exponent

Source: All-Russian 2021/9.2

April 19, 2021
number theoryRussiaAll Russian Olympiad

Problem Statement

Let nn be a natural number. An integer a>2a>2 is called nn-decomposable, if an−2na^n-2^n is divisible by all the numbers of the form ad+2da^d+2^d, where d≠nd\neq n is a natural divisor of nn. Find all composite n∈Nn\in \mathbb{N}, for which there's an nn-decomposable number.
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