MathDB

Even non-negative integer

Source: Indonesia National Science Olympiad 2012 D1 P1

September 4, 2012

number theoryleast common multiplegreatest common divisornumber theory proposed

Problem Statement

Show that for any positive integers

a

and

b

, the number

n=\mathrm{LCM}(a,b)+\mathrm{GCD}(a,b)-a-b

is an even non-negative integer.
Proposer: Nanang Susyanto