MathDB

Let

a

and

n

be positive integers such that: 1.

a^{2^n}-a

is divisible by

n

, 2.

\sum\limits_{k=1}^{n} k^{2024}a^{2^k}

is not divisible by

n

.
Prove that

n

has a prime factor smaller than

2024

.
Proposed by Shantanu Nene

8