Solving the legendary problem #6 - International Math Olympiad 1988 - P6

Here is the reasoning behind the so called "legendary problem #6", which was popularized by Engel in his Problem Solving Strategies book. It's a very good problem for the time and here we'll look at how we'd solve it if we had never seen the trick before.

A couple of things you need to solve this problem:
- a decent understanding of divisibility
- the tenacity to play with a lot of small cases and think about the problem
- POTENTIAL SPOILER: a minimal understanding of the extremal principle (pun very much intended)

Even with the spoiler you're not significantly better equipped to solve this problem as opposed to someone who didn't see the hints. You might be worse equipped if you try and try to apply some extremal principle without playing with the problem and thinking about it by yourself.

With all of that out of the way, let's solve this lovely problem.

[ShefsofProblemSolving]

Here is the reasoning behind the so called "legendary problem #6", which was popularized by Engel in his Problem Solving Strategies book. It's a very good problem for the time and here we'll look at how we'd solve it if we had never seen the trick before.


A couple of things you need to solve this problem:
- a decent understanding of divisibility
- the tenacity to play with a lot of small cases and think about the problem
- POTENTIAL SPOILER: a minimal understanding of the extremal principle (pun very much intended)


Even with the spoiler you're not significantly better equipped to solve this problem as opposed to someone who didn't see the hints. You might be worse equipped if you try and try to apply some extremal principle without playing with the problem and thinking about it by yourself.


With all of that out of the way, let's solve this lovely problem.

[andreben]

It's so commendable to have solved the "legend" as if you didn't know Vieta jumping. You went through some suffering with those algebraic manipulaitions XD

[shreyathebest]

Mate, how do you record your videos? I need some help. You use a stand?