# A simple doubt in number theory problem for an even number,

by monalisa   Last Updated April 15, 2019 11:20 AM

I considered an even number $$n\geq 9$$, where it is divisible by some positive integer $$k$$.

Also, $$k$$ does not divide $$\frac{n}{2}$$.

Let $$n = kq$$.

Can we say that $$q$$ is even in this case? Can anyone help to get it theoretically? Thanks a lot for the help.

My attempt:

Let $$n = kq$$.

Since $$k$$ does not divide $$\frac{n}{2}$$, we have

$$n/2 = k.q_1 + r$$ for $$0.

How to conclude the even or odd property of $$k$$ and $$q$$ here?

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#### Answers 1

As a counter example, take $$n = 14$$ and $$k = 2$$. Then $$2$$ does not divide $$14/2 = 7$$ and $$q = 7$$ is not an even number.

ArsenBerk
April 15, 2019 11:18 AM