Question

Prove that, if x and y are positive irrationals such that
1
x
+
1
y
= 1;
then the sequences [x]; [2x]; [3x]; : : :; [y]; [2y]; [3y]; : : : together
include every positive integer exactly once.
Note: [u] denotes the largest integer n satisfying n  u.

Answer 1

anyone...