Question

Prove that if n is a positive integer such that the sum of the divisors of n is n+1, then n is prime.

Short answer

n is prime

Step-by-step solution

Step 1:

N has at least two divisors, namely, 1 andwhose sum is n + 1.

If it has other divisors then the sum of its divisors becomes strictly bigger thann + 1 .

But we are given that the sum of its divisors is n + 1 , which implies that n has only two divisors 1 and n which implies that n is prime.