设 p,q 为质数,且 p^3+q^3+1=p^2q^2,求 (p,q)
问题描述：
设 p,q 为质数,且 p^3+q^3+1=p^2q^2,求 (p,q)
答
首先若p = q, 有2p³ = p^4-1 = (p-1)(p+1)(p²+1), 右端各项均不被p整除, 矛盾.不妨设p 2, 则由q > p有q > p+1.将原...
设 p,q 为质数,且 p^3+q^3+1=p^2q^2,求 (p,q)
首先若p = q, 有2p³ = p^4-1 = (p-1)(p+1)(p²+1), 右端各项均不被p整除, 矛盾.不妨设p 2, 则由q > p有q > p+1.将原...