讨论了丢番图方程3n+px2=yp(x,y,n∈N；p是奇素数)的可解性,得到以下结果:(1)当p=3时,方程的所有解为(x,y,n)=(46·33t+1,13·32t+1,6t+7),(10·33t+1,7·32t+1,6t+8).(2)当p=1(mod 24)时,方程没有解.%The solvability of Diophanine equation 3n+px2=yp was investigated in this paper.If p=3,the equation has only solution(x,y,n)=(46·33t+1,13· 32t+1,6t+7),(10·3t+1,7·32t+1,6t+8).Ifρ(=)1(mod 24),then the equation has no solution.
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