Given an integer $n$ and an irrational $r$, $n>r$, $n-r$ is irrational but $r + (n - r)$, the sum of two positive irrationals, is an integer. Is that the only way that two irrationals can sum to an integer?
What if the question is rephrased using rationals instead of integers? Is the only way two irrationals can sum to a rational is by using the form $r + (a/b - r)$?
Can $r_{1} + (a/b - r_{2})$ ever be a rational? An integer?