关于指数丢番图方程P^m=q^n+2~h

ON THE EXPONENTIAL DIOPHANTINE EQUATION P^m=q^n+2~h

本文考虑丢番图方程P^m=q^n+2~h, (p.q是不同素数)的非负整数解问题,给出了方程无解的若干充分条件,所得结果不同于文〔3〕.〔4〕.〔5〕.〔6〕.〔7〕的有关结论。

Let p.q be district primes. the author proves the fllowing result: Th_1.lf p=qt^2±16, Then the equation p^m=q^n+16 has only solution m=1, t=q^k, n=2k+1. Th_2, lf p=qt^2+16(t≠3), then the equation p^m=q^n+2 has no integer Solultion m,n. Th_3. lf P=qt^2+16(t≠3), then the equation p^m=q^n+4 has no interger Solution, m,n. Th_4,lf p=q+16, then the equation P^m=q^n+8 has no integer Solution, m,n. Th_5lfp=q+16, then the equation p^m=q^n+2~h has no integer Solution m,n. with h≥5.