# Mistakes Give Rise To Problems-19

Algebra Level 4

We know the following property of exponents that:

$\left(\dfrac{a}{b}\right)^{c}=\dfrac{a^{c}}{b^{c}},$

but we can't do this in factorials as:

$\left(\dfrac{a}{b}\right)!=\dfrac{a!}{b!}$

In general, doing this will be a Big Mistake. However, this holds for certain integers $$a$$ and $$b.$$ For how many ordered pairs of integers $$(a,b)$$ where $$1≤b≤a≤100$$ does this hold?

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