Conjecture. If a1+...+an-1=an, (ai, aj)=1, i<>j, i=1,2,3,...n, j=1,2,3,...,n, then there exists p prime number such that p|a1...an, p^n†a1...an.
Counter-example of Papava's conjecture:
271³+2³73³3^5=919³.
See other variant of Papava's conjecture.
I wait commentary
Emzar Papava