Logic. Express the proposition in symbols

Question

Assume we are dealing only with integers.

Using only numerals, variables, logical symbols and the mathematical symbols, I need express the following proposition:

$$100 \text{ is a multiple of } 5 $$

I've tried it, and, in my own words I came up with:

If n is a multiple of 100 then 100 is multiple of 5.

Trying to see if this is right.

Answer 1

"$100$ is a multiple of $5$" by definition:

$$\exists\, x\in \mathbb Z \;( \,5x = 100\,)$$

And we can verify that statement is true by showing the existence of such an integer x:

$$5x= 100 \iff x = \frac{100}{5} = 20, $$ noting that the one and only integer satisfying $5x = 100$ is $x=20$.

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Note that there is another way with which to express "$100$ is a multiple of $5$" $\iff$ "$5$ is a divisor of $100$." The notation used to express "$5$ divides $100$" is given by $$5\mid 100$$ And the logical definition given above expresses as much.

Answer 2

We have,

n = 100k

= 5(20k)

So 100 is a multiple of 5.

Answer 3

I assume you need it in logic:

$\exists x : 100 = 5 * x$