Subcontests
(6)a and b coprime, prove if (a^s + b^s)|(a^r + b^r), then s|r
Let a,b,r, and s be positive integers (a≤2), where a and b have no common prime factor.
Prove that if ar+br is divisible by as+bs, then r is divisible by s. Given n integers, sum = 0, product = n, find all n.
It is known that there are n integers a1,a2,⋯,an such that
a1+a2+⋯+an=0anda1×a2×⋯×an=n.
Determine all possible values of n. [IMONST2 2022 Primary #2] Number sequence
The following list shows every number for which more than half of its digits are digits 2, in increasing order:
2,22,122,202,212,220,221,222,223,224,…
If the nth term in the list is 2022, what is n?