MathLabs

Problem 5

Does there exist a positive integer n n such that n n has exactly 20002000 distinct prime divisors and n n divides 2n+12^n+1?
Step 4 of 5: Preserve divisibility
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n∣2n+1⟹np∣2np+1.n\mid2^n+1\Longrightarrow np\mid2^{np}+1.
Detailed analysis

Modulo n use that p is odd; modulo p use p congruent to 1 modulo 2n, then apply the Chinese remainder theorem.