Question 61
A positive integer is called *nice* if it is equal to the sum of the fourth powers of certain five distinct its divisors. (A divisor may be equal to $1$ or to the number itself.)
a) Prove that any nice number is divisible by $5$.
b) Are there infinitely many nice numbers?
a) Prove that any nice number is divisible by $5$.
b) Are there infinitely many nice numbers?