Find all integers x for which there exists an integer y such that 1/(x)+1/(y)=1/7 (in other words, find all ordered pairs of integers (x, y) that satisfy this equation, then enter just the s's from these pairs.)

Mellie Aug 2, 2016

#1**+1 **

1/x + 1/y = 1/7 simplify

[x + y ] / xy = 1/7

7[x + y] = xy

7x + 7y - xy = 0 rewrite as

xy - 7x - 7y = 0 add 49 to both sides

xy - 7x - 7y + 49 = 49 factor

(x - 7) ( y - 7) = 49 (1)

Note that the following ordered pairs of integers would work :

(14, 14)

(8, 56)

(56, 8)

(-42, 6)

(6, -42)

Note that (0,0) would also satisfy (1), but ...... x and y cannot be 0 in the original problem [division by 0 ]

CPhill Aug 2, 2016