Question

Show that any three integers contain a pair whose sum is even.

Answer 1

let the first integer be n
the next one is n+1
and the last one is n+2

Answer 2

if the first integer is even then so will be n+2
OR
if the first integer is odd then n+2 will be odd too

Answer 3

the sum of two even number is an even number,

and the sum of two odd number is also an even numbers

so in either case , there will necessarily be a pair that gives an even number when summed

Answer 4

WhatJRharrison92 is asking...any three integers...not necessarily consecutive integers.

But the argument is similar for ANY three integers.

Answer 5

Yes ANY three not consecutive.

Answer 6

Well, it says any integers, consecutive or not...but Unkle...will finish that argument for ANY integers.

Answer 7

ok

Answer 8

oh, right, thought the question said consecutive.

Answer 9

well, if you have three nonconsecutive integers,

each of them must be either even or odd,

in any combination, there will be sum that is even