MathDB

Consider rows of the form:

[x], [2x], [3x], ...

Proof that, if

N \in N

does not occur in the sequence

([n x])

, then there is an

n \in N

with

n - 1 < \frac{N}{x}< n -\frac{1}{x}

Prove that, for

x, y \notin Q

\frac{1}{x}+\frac{1}{y} = 1

, then each

N \in N

term is either of

([nx])

or of

([ny])

5