Italy - Math Olympiad Problem | Find all integer solutions

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[@oliviervancantfort5327]

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.

[@MajesticUC]

I agree

[@hippopotamus_nr2587]

can't that simply be fixed by saying (x+y) = c and (x-y) = 17/c for all c's element of ]-sqrt(17), 0[ union ]sqrt(17), +inf[
and then giving an answer for x and y in terms of c
might be wrong what i'm saying tho

[@SG49478]

You are absolutely right. I don't know if this is the same person, but a few months ago the same problem was posted here on youtube with the exact same wrong method to solve it.
The fact that he found one solution is simply pure luck. This method didn't even find the second solution, which is (18;1). Not even to mention that this method does not prove there aren't any more solutions.

[@alimahmoudifar4772]

Yes

[@qehn]

Also (18, 1) and (1, -16)

[@mauriziograndi1750]

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

[@donsena2013]

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

[@Itesh.R]

no
a= 18 b= 1

[@RealQuInnMallory]

(1)^1 ➖ (17)^1 (b ➖ 17a+1)

[@subudhitech1550]

(18^1)-(1^18)

[@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?

[@brossolletpaul5905]

Why x and y natural ?

[@prithvichidri9634]

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

[@subudhitech1550]

We can break the 17 to get 18^1-1^18

[@raviyadav031]

India 🎉

[@onkotonkoblu]

Hi, from Italy ❤🤍💚

[@ReginaldCarey]

I can’t get past the horrible penmanship.

[@enantiodromia]

Then superficiality prevents you from learning. What a pity.

[@ReginaldCarey]

No, the answer was easy to compute - for me. If your handwriting is poor, then type. Don’t force your viewers/students to struggle unnecessarily. That’s not good teaching.