Number Theory Problem from The Maclaurin Olympiad | Math Olympiad Training

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Can you solve this number theory problem from the U.K Maths Olympiad?

This problem comes from the 2017 Maclaurin Olympiad in the U.K for 15/16-year-old students.

Did you solve it?
Let me know in the comments how you solved this problem. I’d love to hear about it!

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Maths videos by Giuliano Grasso - mathematics graduate from the University of East Anglia.

I post weekly maths olympiad videos for you to try and solve.

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I made the substitution a=m^2, b=n^2 and then used the quadratic formula to get the same solutions.

rtdavis
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After separating variables add 16 to both sides and simplify

SrisailamNavuluri
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why when you square root you get +- (n^2 - 4) but not do the same for the LHS of the equation?

wiktor