document.write( "Question 1070274: Prove that the product of two odd numbers is odd, using an indirect proof and a proof by contradiction. \n" ); document.write( "

Algebra.Com's Answer #685426 by josgarithmetic(39617) $\"\"$ $\"About$

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Here are two odd numbers.
\n" ); document.write( "2n+1, and 2n-1, for some integer, n.\r
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\n" ); document.write( "\n" ); document.write( "We believe that (2n+1)(2n-1) will be 'even', and we can simplify the product expression, through multiplication:
\n" ); document.write( " $\"2n%2A2n%2B2n-2n-1\"$
\n" ); document.write( " $\"4n%5E2-1\"$
\n" ); document.write( "But, is this 'even', or not?\r
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\n" ); document.write( "\n" ); document.write( "The $\"4%2An%5E2\"$ is undoubtedly EVEN. To that is subtracted the ODD number, 1, which together makes 4n^2-1, the product of the two odd numbers, an ODD number. \n" ); document.write( "

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