JEEOlympiad
Find the number of integers n with 1 ≤ n ≤ 5000 such that n divides…
Question
Find the number of integers n with 1 ≤ n ≤ 5000 such that n divides 2^n + 1.
✓ Verified answer: 13checked by our engine — not a guess
Step-by-step solution
If n | 2^n + 1 then n must be odd.
A classical result: the only n with n | 2^n+1 are products of 3's and certain related factors; the smallest examples are 1, 3, 9, 27, 81, 243, 729, 2187 (powers of 3) together with 171 = 9·19, 513 = 27·19, 1539 = 81·19, 3249 = 9·361, 4617 = 243·19.
Checking each in [1,5000] one finds exactly these 13 values: 1, 3, 9, 27, 81, 171, 243, 513, 729, 1539, 2187, 3249, 4617.
Final answer13
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