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JRHarrison90

  • one year ago

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

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  1. UnkleRhaukus
    • one year ago
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    let the first integer be n the next one is n+1 and the last one is n+2

  2. UnkleRhaukus
    • one year ago
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    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

  3. UnkleRhaukus
    • one year ago
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    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

  4. Easyaspi314
    • one year ago
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    WhatJRharrison92 is asking...any three integers...not necessarily consecutive integers. But the argument is similar for ANY three integers.

  5. JRHarrison90
    • one year ago
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    Yes ANY three not consecutive.

  6. Easyaspi314
    • one year ago
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    Well, it says any integers, consecutive or not...but Unkle...will finish that argument for ANY integers.

  7. JRHarrison90
    • one year ago
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    ok

  8. UnkleRhaukus
    • one year ago
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    oh, right, thought the question said consecutive.

  9. UnkleRhaukus
    • one year ago
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    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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