Question

证明对于正整数x,y ,方程 (x!)(y!) = +y!仅有唯一解x=y=2

Answer 1

证明：

(x!)(y!) = x!+y!

(x!)(y!) - x!-y!+1=1

(x!-1)(y!-1)=1

因为X,Y都是正整数,所以X!-1与Y!-1均大于等于0,且为整数,

即X!-1=1/(Y!-1)>=0,Y!-1=1/(X!-1)>=0,所以X=Y=2