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Find all positive integers x such that there exists a positive integer y satisfying: 1/x + 1/y = 1/7
Answer.
1/x + 1/y = 1/7
(x+y)/xy = 1/7
7x + 7y = xy
xy - 7x - 7y = 0
x(y-7) - 7(y-7) = 49
(x-7)(y-7) = 49
Thus satisfying values are:
49 * 1
1 * 49
7 * 7
So values of x and y can be, (42, 8), (8,
42), (14, 14).
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