【摘要】 作者计算出在一定条件下,Jacobi符号((x~a+1)/(x~b-1))总是1,从而可以解释柯召先生在研究偶指数的Catalan猜想时有一种情形最复杂的原因.作为推论,作者证明了一些不定方程没有正整数解.更多还原

【Abstract】 By computing,under some condition,the Jacobi symbol((x+1)/(x~b-1))is always 1,which explains the reason why Prof.Ke Zhao met a complicated case while researching Catalan conjecture of even exponent case.As a corollary,it is proved that some equations have no positive integer solutions.更多还原