一道不定方程试题

aishuxue

tommywong

假设$y-x>0$
$2^{t-x}-2^{y-x}=1$
$t-x=log_2 (1+2^{y-x})>y-x>0$
$0\equiv 1\pmod{2}$矛盾
同理$x-y>0$不成立
$x=y=t-1,a=\dfrac{2t-2}{t}=2-\dfrac{2}{t}\in Z$
$t=-2,-1,1,2$
$M=\{0,1,2,4\}$