document.write( "Question 1208363: Prove that given any set of $17$ integers, there exist nine of them whose sum is divisible by $2.$ \n" ); document.write( "
Algebra.Com's Answer #846739 by Edwin McCravy(20066)\"\" \"About 
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document.write( "The sum of an odd number of odd numbers is always odd, never even\r\n" );
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document.write( "9 is an odd number, so if all 17 were odd, the statement would be false. \r\n" );
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document.write( "However, a question you might ask is whether a set of 17 odd positive integers \r\n" );
document.write( "is the ONLY counterexample, or are there any others?\r\n" );
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document.write( "Certainly 16 odds and 1 even is not a counterexample because 8 odds and 1 even\r\n" );
document.write( "would be 9 with an even sum.\r\n" );
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document.write( "Edwin

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