关于不定方程(n∏(k=1))(k^2+1)=pm^2

On the diophantine equation (n∏(k=1))(k^2+1)=pm^2

设p为奇素数.对于不定方程(n∏(k=1))(k2+1)=pm2,证明了当p<9 985 600且p≠17时,此方程无正整数解.

Let p be odd prime. For the Diophantine equationnⅡk=1（k^2＋1）=pm^2, we proved that when p〈9 985 600 withp≠17, then this equation has no positive integral solution.