Problem of the Fortnight #2
Mind
the Gap!
Prove that, among the positive numbers
a, 2a, 3a, 4a, … , (n-1)a
there is at least one that differs from an integer by at most 1/n.
Recall
that an integer is an element from the set {… , -2,
-1, 0, 1, 2, …}
Solutions are due by