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 #685431 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "The \"proof\" by josgarithmetic\" is wrong starting from his second line.\r
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\n" ); document.write( "\n" ); document.write( "The correct proof is this:\r
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document.write( "Let assume that the product of two odd numbers, m and n, is an even number N:  N = m*n.\r\n" );
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document.write( "Then this even number N is a multiple of 2.\r\n" );
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document.write( "The number 2 is a prime number.\r\n" );
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document.write( "Since 2 divides N, it must divide at least one of the factors, n or m.\r\n" );
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document.write( "If 2 divide n, then n is and even number. It contradicts to the original assumption that n is odd.\r\n" );
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document.write( "If 2 divide m, then m is and even number. It contradicts to the original assumption that m is odd.\r\n" );
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document.write( "This/these contradiction/contradictions proves/prove that the product of two odd numbers is an odd number.\r\n" );
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\n" ); document.write( "\n" ); document.write( "QED. Proved and solved.\r
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