Question 28

The number of integer pairs $$(m,n)$$ such that $$m(n^2+1)=48$$ is ______.

Correct Answer: 3

Solution

Since $$n^2+1$$ must divide $$48$$, check the divisors of $$48$$ that are one more than a perfect square. The possibilities are $$n^2+1=1$$ and $$n^2+1=2$$, giving $$n=0,1,-1$$. Each value determines one integer $$m$$, so there are $$3$$ ordered pairs.

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