# An Interesting Expansion Product

\begin{aligned} (x+1)^p(x-3)^q = x^n+a_1x^{n-1}+a_2x^{n-2}+\cdots+a_n \end{aligned} Consider the expansion above where $$a_1, a_2, \cdots, a_n, p$$ and $$q$$ are integers with $$p$$ and $$q$$ positive and $$n = p+q$$. How many ordered pairs $$(p, q)$$ with $$1\leq p, q < 1000$$ are there such that $$a_1 = a_2$$?

×

Problem Loading...

Note Loading...

Set Loading...