Subcontests
(4)a_{n+1} - a_n = n(a_n - 1)
The sequence of positive integers a0,a1,a2,... is defined by a0=3 and an+1−an=n(an−1) for all n≥0. Determine all integers m≥2 for which gcd(m,an)=1 for all n≥0. an^k, bn^{\ell} , cn^m are sidelengths of a triangle
Determine all positive integers n with the following property: for each triple (a,b,c) of positive real numbers there is a triple (k,ℓ,m) of non-negative integer numbers so that ank, bnℓ and cnm are the lengths of the sides of a (non-degenerate) triangle shapes.