MathDB

At least one of x or y is integer - [Iran Second Round 1985]

Source:

December 28, 2010

floor functionnumber theory proposednumber theory

Problem Statement

Let

x

and

y

be two real numbers. Prove that the equations \lfloor x \rfloor + \lfloor y \rfloor =\lfloor x +y \rfloor , \lfloor -x \rfloor + \lfloor -y \rfloor =\lfloor -x-y \rfloor Holds if and only if at least one of

x

y

be integer.

Back to Problems View on AoPS