Problems & Puzzles: Puzzles

Puzzle 527. sigma(x) = 1 (mod x)


Farideh Firoozbakht sent the following puzzle:

It is obvious that all primes are solutions for the following equation.

sigma(x) = 1 (mod x) (*)

Q. Can you find a composite solution for (*) ?

 

Antoine Verroken wrote:

According to R. Guy and G. Cohen numbers with sigma(x) = 2 * x + 1 have been called quasiperfect numbers ( they are abondant numbers sigma(x) > 2*x ). If there exists it must be an odd square number > 10^35 and have at least 7 distinct prime factors. It is relatively easy to prove that there exists no composite x for x = p * q and x = p * q * r ( p,q,r primes ) with sigma = k * x + 1.

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