document.write( "Question 1189131: Use direct proof to prove that the sum of two odd integers say a and b is even. Note
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Algebra.Com's Answer #820383 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "Use direct proof to prove that the sum of two odd integers say a and b is even. Note
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document.write( "Let \"a\" and \"b\" be odd integer numbers.\r\n" );
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document.write( "Then, as you discussed earlier,  a = 2n+1, b = 2m+1  for some integer numbers \"m\" and \"n\".\r\n" );
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document.write( "It implies that  a + b = (2n+1) + (2m+1) = 2n + 1 + 2m + 1 = 2n + 2m + 2 = 2*(n+m+1).\r\n" );
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document.write( "Thus the sum a + b is an integer number of the form 2k, where integer number \"k\" is n+m+1.\r\n" );
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document.write( "It means that  a + b  is an even number.\r\n" );
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