1/m+1/n=1/7
⇔$\frac{m+n}{mn}$ = $\frac{1}{7}$
⇔ mn = 7m + 7n
⇔ ( m - 7 ) ( n - 7 ) = 49
mà m,n ≥ 0 ( m,n nguyên dương )
⇒ 9 m - 7 ) ; ( n - 7 ) ≥ -7
Mặt khác: 49 = 49.1 = 7.7 = −7.(−7) =−49.(−1)
⇒ [$\left \{ {{m-7=49} \atop {n-7=1}} \right.$ => [$\left \{ {{m=56} \atop {n=8}} \right.$
[$\left \{ {{m-7=1} \atop {n-7=49}} \right.$ => [$\left \{ {{m=8} \atop {n=56}} \right.$
[$\left \{ {{n-7=7} \atop {m-7=7}} \right.$ => [$\left \{ {{m=14} \atop {n=14}} \right.$
[$\left \{ {{m-7=-7} \atop {n-7=-7}} \right.$ => [$\left \{ {{m=0} \atop {n=0}} \right.$
