# Topsy-turvy

Algebra Level 4

Let's begin with an equation: $x_1+y_1=n$ ($$n$$ is a positive integer)

That's too boring, so let's add some numbers, let's make 5, 4, 4 and 2 as the main protagonist: $5x_2+4y_2=n^{4-2}~~~~~~(1)$ Unfortunately, someone came and messed up the numbers, making a new equation: $x_3^4+5y_3=n^4-2~~~~~~(2)$ If there are $$p$$ ordered pairs of non-negative integer solutions $$(x,y)$$ that satisfies $$(1)$$, there are $$q$$ ordered pairs of non-negative integer solutions $$(x,y)$$ that satisfies $$(2)$$, and $$\vert p-q\vert=9$$, what is the value of $$n$$?

This is one part of 1+1 is not = to 3.

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