Hello !

Here is your question in LaTeX language (click on it to see the code) :

Let this number be N.

The first reflex will be "We may be able to do it by induction". Nope, the numbers are such that it will be difficult (if not impossible).

I hope you're familiar with using modulus.

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Note that

Since 8 and 251 are coprime, if a number is divisible by 8 and 251, then it is divisible by 2008.

We'll study the numbers modulo 8.

Therefore

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Now, does 251 divide N ?

Therefore

And we're done !