document.write( "Question 207719: What is the counter example of \"The sum of any 2 odd numbers is even?\" \n" ); document.write( "

Algebra.Com's Answer #157114 by jim_thompson5910(35256) $\"\"$ $\"About$

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There's a problem with your question. There are no counter examples to prove the statement \"The sum of any 2 odd numbers is even\" wrong. \r
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\n" ); document.write( "\n" ); document.write( "It turns out that any odd number can be written in the form $\"2x%2B1\"$ where 'x' is a whole number. Now let's say we have two odd numbers $\"y=2a%2B1\"$ and $\"z=2b%2B1\"$ where 'a' and 'b' are whole numbers. If we add them up, we get: $\"y%2Bz=%282a%2B1%29%2B%282b%2B1%29=%282a%2B2b%29%2B2=2%28a%2Bb%29%2B2=2%28a%2Bb%2B1%29=2k\"$ where $\"k=a%2Bb%2B1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now because even numbers fit the form $\"2x\"$ , where 'x' is a whole number, this means that $\"2k\"$ is an even number (since 'k' is a whole number). \r
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\n" ); document.write( "\n" ); document.write( "So it turns out that the sum of ANY two odd numbers is ALWAYS even. This is why no counter examples are possible. \n" ); document.write( "

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