五个具有固定素因子个数的整数之平方和

On Sums of Five Squares with a Fixed Numbes of Prime Factors

设N≡5(mod24)为充分大的正整数,若GRH(广义Riemann假设)成立, 则方程N=n12+n22+…+n52有解,此处ni,i=1,2,…,5具有固定素因子个数,并且方程解数具有渐近式．

Let N ≡ 5 （rood 24） be a sufficiently large positive integer. Assume GRH （the generalized Riemann hypothesiis）, then the equation N ： n1^2 ＋ n2^2 ＋... ＋ n5^2 has solutions, where hi, i = 1, 2,..., 5 has a fixed number of prime factors. Futhermore, an asymptotic formula for the number of solutions is obtained.