Question 1070274
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The "proof" by josgarithmetic" is wrong starting from his second line.


The correct proof is this:


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Let assume that the product of two odd numbers, m and n, is an even number N:  N = m*n.


Then this even number N is a multiple of 2.


The number 2 is a prime number.


Since 2 divides N, it must divide at least one of the factors, n or m.


If 2 divide n, then n is and even number. It contradicts to the original assumption that n is odd.


If 2 divide m, then m is and even number. It contradicts to the original assumption that m is odd.


This/these contradiction/contradictions proves/prove that the product of two odd numbers is an odd number.
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QED. &nbsp;&nbsp;Proved and solved.