SOLUTION: The difference between the squares of two positive integers is 376 and their positive difference is as small as possible. What is the value of their positive difference?

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Question 900033: The difference between the squares of two positive integers is 376 and their positive difference is as small as possible. What is the value of their positive difference?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two positive integers be p and q, p > q

p² - q² = 376

(p-q)(p+q) = 376

So (p-q) and (p+q) are two integers, (p-q) < (p+q),
whose product is 376.  The only pairs of factors
with product 376 are

1,376
2,188
4,94
8,47

So we have 4 possible systems of equations:

system%28p-q=1%2Cp%2Bq=376%29,system%28p-q=2%2Cp%2Bq=188%29,system%28p-q=4%2Cp%2Bq=94%29,system%28p-q=8%2Cp%2Bq=47%29

The solution to the first system is (p,q) = (188.5,187.5),
and those aren't even positive integers.  So the smallest
possible positive difference of p and q can't be 1.

The solution to the second system is (p,q) = (95,93), and
the positive difference of them is 2.  So that's the answer.
We don't need to solve the other two systems, since p and q
differ by more than 2 in those.

Answes:  It's the positive difference of 95-93, which is 2.

Edwin