Abstract: Let p be an odd prime,a and b be coprime positive integers with a>b,gcd(a,b)=1.more over let f(a,b,p)=(ap-bp)/(a-b).Using some elementary number theory methods,it is proved that if log a≤max(7log p,(2p-1-1)log p),f(a,b,p) is not an odd perfect number.

Key words: generalized Mersenne number, odd perfect number, lower bound