G.360 odd number multiplying — Heath

IX.29

If an odd number by multiplying an odd number make some number, the product will be odd.

For let the odd number A by multiplying the odd number B make C ;

I say that C is odd.

For, since A by multiplying B has made C,

therefore C is made up of as many numbers equal to B as there are units in A. [G.269]

And each of the numbers A, B is odd;

therefore C is made up of odd numbers the multitude of which is odd.

[G.354]Thus C is odd.

Q. E. D.

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