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**Let . Then show that x is an integer. (Hint: First show that x is a rational number)**

is an integer

is also an integer.

Hence ratio of those two are is a rational.

Again are rational. Also it is given that is integer. Hence is rational.

Therefore is rational. Since ratio of rationals is rational.

Suppose x = p/q, then where gcd(p, q) = 1 and k is an integer.

But this implies q divides p which means q = 1.

Hence x is an integer. (Proved)

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[…] Let . Then show that x is an integer. (Hint: First show that x is a rational number) Solution […]