数论好像是2^x减3^y为1,求x,y(x,y为正整数)求所有x,y

Question

数论好像是
2^x减3^y为1,求x,y (x,y为正整数)
求所有x,y

Answer 1

2^x-3^y=1,有2^x=3^y+1.当y为偶数时,2^x=3^y+1=9^(y/2)+1=(8+1)^(y/2)+1=8m+1+1=8m+2,故x=1,此时有y=0,不满足题意.当y为奇数时,2^x=3^y+1=(3+1)(3^(y-1)+3^(y-2)+……+3+1),注意到(3^(y-1)+3^(y-2)+……+3+1)为y个（...