关于Sophie Germain素数的Diophantine方程(x^p-1)/(x-1)=qy

Diophantine Equation(x^p-1)/(x-1)=qy Concerning Sophie Germain Primes

设p和q=2p+1都是奇素数,运用初等数论方法证明了方程(xp-1)(x-1)=qy有无穷多组正整数解(x,y),并且给出了该方程解数的渐近估计。

Let p and q = 2p ＋ 1 be odd primes. Using some elementary number theory methods ,we prove that the equation （x^p-1）/（x-1）=qy has infinitely many positive integersolution （x,y） . Moreover,an asymptotic estimation for the number of solutions of the equation is given.