International Math Olympiad

International Math Olympiad | 1998 Q6.

Рет қаралды 30,903

3 жыл бұрын

We look at a solution to question 6 from the 1998 International Mathematical Olympiad. This problem involves a functional equation.
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Пікірлер: 219

@MichaelPennMath 3 жыл бұрын

Ok guys, I was out climbing today and saw the comments about my sketchiness with the inequality argument. Here is a fix.... Around

@hfix307 3 жыл бұрын

Goodness, this is a brutal question. Props to people who solved this in test conditions.

@Monolith-yb6yl 3 жыл бұрын

There is a mistake: first using of equasion 1 to prove "almost multiplicative" property. Have to be n =a, m=f(b^2 f(1))

@brettaspivey 3 жыл бұрын

This one was pretty botched, better try again

@HagenvonEitzen 3 жыл бұрын

The problem is much simpler for those considering 0 a natural number ;)

@HagenvonEitzen 3 жыл бұрын

At the end, you forgot to mention that every involution of the set of primes gives rise to a valid g. Otherwise, it might happen that 120 cannot be achieved

@thephysicistcuber175 3 жыл бұрын

The answer is zero. Next please.

@theartisticactuary 3 жыл бұрын

Not only were there errors here (like the subtraction of inequalities) but this seems to be at about double your normal feed, making it really difficult to follow. One minute we're solving quadratic equations very slowly using a formula, the next minute I'm having to keep pausing the video.

@adandap 3 жыл бұрын

I have more chance of running a sub 10 second 100m in the "other Olympics" than I have of solving that problem under test conditions!

@lucassandleris4486 3 жыл бұрын

You can't just subtract inequalities like that... A way of proving r≥s is to show by induction that f(a)ⁿ=f(1)^(n-1).f(aⁿ), then nr≥(n-1)s for all n, so r/s≥(n-1)/n, but letting n approach infinity we get r/s≥1 and therefore r≥s.

@dimitrisstam7596 3 жыл бұрын

Excellent content

@DerZerberster1 3 жыл бұрын

I think, there is a mistake at

@wesleydeng71 3 жыл бұрын

25:40

@andreivila7607 3 жыл бұрын

Finally! I’ve been waiting for one of those for a long long time. Nice problem, and I hope you will do more of them. Have a fantastic day!

@adityaprakashsingh2675 3 жыл бұрын

I think there is an error at ~

@HagenvonEitzen 3 жыл бұрын

25:15

@andreben6224 3 жыл бұрын

Wow this one was brutal. There were some mistakes along the way too, but in the end, it all holds together, even though I feel one should show that the minimum possible value can be attained by some function f (or g, since the g function will also verify (1)).