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

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

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Other answers:

WhatJRharrison92 is asking...any three integers...not necessarily consecutive integers. But the argument is similar for ANY three integers.
Yes ANY three not consecutive.
Well, it says any integers, consecutive or not...but Unkle...will finish that argument for ANY integers.
oh, right, thought the question said consecutive.
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

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