anonymous
  • anonymous
Show that any three integers contain a pair whose sum is even.
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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UnkleRhaukus
  • UnkleRhaukus
let the first integer be n the next one is n+1 and the last one is n+2
UnkleRhaukus
  • UnkleRhaukus
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
UnkleRhaukus
  • UnkleRhaukus
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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anonymous
  • anonymous
WhatJRharrison92 is asking...any three integers...not necessarily consecutive integers. But the argument is similar for ANY three integers.
anonymous
  • anonymous
Yes ANY three not consecutive.
anonymous
  • anonymous
Well, it says any integers, consecutive or not...but Unkle...will finish that argument for ANY integers.
anonymous
  • anonymous
ok
UnkleRhaukus
  • UnkleRhaukus
oh, right, thought the question said consecutive.
UnkleRhaukus
  • UnkleRhaukus
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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