Mistakes Give Rise To Problems-19

Algebra Level 4

We know the following property of exponents that:

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

but we can't do this in factorials as:

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

In general, doing this will be a Big Mistake. However, this holds for certain integers aa and b.b. For how many ordered pairs of integers (a,b)(a,b) where 1ba1001≤b≤a≤100 does this hold?

Try this too.

×

Problem Loading...

Note Loading...

Set Loading...