Italy - Math Olympiad Problem | Find all integer solutions

You should know this trick. If you're reading this ❤️.

What do you think about this problem?

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[JohnBames]

The method is wrong.
There is no reason why x and y should still be integers as square roots were introduced in their definition. Therefore, decomposing 17 in prime factors is not a justified step.

[mauriziograndi]

a=3 = b=4
3^4=81 - 4^3=64
81-64=17
We appreciate the explanation but in this case the result was easily found by inspection.

[unebonnevie]

The question would be much harder to find all solutions for *a* and *b* such that they would satisfy the original equation. The video shows ONE solution.

[pidigi]

2:38 why x + y > x- y? It’a valid only for y>0

[donsena]

With two unknowns defined by only one equation, there is going to be a family of solutions for a & b -- especially if we allow for non-integer values of a & b

[unebonnevie]

I don't understand the logic/thinking of getting into the inequality of *(x + y) > (x - y)* and becoming two equations, *(x + y) = 17 and (x - y) = 1* . How is that allowed?

[prithvichidri]

Guys who tried adding something to 17 to get a perfect square or perfect cube etc.🤙 and get the ans

[ReginaldCarey]

I can’t get past the horrible penmanship.