document.write( "Question 706285: use expressions for odd integers to confirm the conjecture that the product of two odd integers is an odd integer. \n" ); document.write( "

Algebra.Com's Answer #435120 by josgarithmetic(39617) $\"\"$ $\"About$

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n is any natural or whole number.
\n" ); document.write( "Even Integer: 2n
\n" ); document.write( "Odd Integer: 2n+1\r
\n" ); document.write( "\n" ); document.write( "Let m be any whole number.
\n" ); document.write( "(2(n)+1)(2(n+m)+1)
\n" ); document.write( "4n(n+m)+2(n+m)+2n+1
\n" ); document.write( "=2(2n(n+m)+(n+m)+n)+1\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Notice very carefully that the expression inside the outermost parentheses,
\n" ); document.write( "2n(n+m)+(n+m)+n, is a whole number, we may call N, so that
\n" ); document.write( "we have 2N+1. This is an odd number. Proved! \n" ); document.write( "

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