丢番图方程x^(2p)-Dy^2=1与费马商Q_p(m)(英文)

The Diophantine Equation x^(2p)-Dy^2=1 and the Fermat's Quotient Q_p(m)

0 The Diophantine equation X^(2p)-Dy^2=1Let D be a positive integer which is square free,and p be a prime.In 1966,Ljunggren showed that if p=2 and D=q is a prime,then the Diophantine equationx^(2p)-Dy^2=1(1)has only positive integer solutions(q,x,y)=(5,3,4),(29,99,1820).In 1979,KoChao and Sun Qi showed that if p=2 and D=2q,then Eq.(1)has no positive inte-