The Russian | Diophantine Equation | Russian Math Olympiad

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

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[GGMaths]

A follow up question is to consider the equation x^k + y^k = p^n, where (x, y) = 1, n > 1 and p is a prime > 2. Can you prove that k is a power of p? You can use a similar method used in the video.

[onlypuremathematics]

Many many thanks to you sir your best explanation of this types of problems. Sir I wish to know that if you will discuss about Eular's famous 4th power taxicab number parametric solution. X^4+Y^4 =P4+Q^4 How to solve this problem?

[alessandrofenu]

Good video for starter! More intuitive solution comes from using LTE lemma and an easy estimate on x and y

[VerSalieri]

Can you please explain why 3 divides k implies that k=3? Shouldn’t it imply that k=3s for some s? or are we again using some sort of infinite decent s?

[particleonazock]

This looks very much like a problem similar to previous ones I solved, but I can't pinpoint the exact problem. Unfortunately, I could not solve it. I'll try again in a week.

[kshitijjain]

How k=3 (K should be an odd multiple of 3 rather than k=3)

[shreyamjha]

Thanks for solving this problem(which I suggested) ｡◕‿◕｡, the explanation was quite crisp and clear..

[tonyha]

Can you explan @3:55 why 3^(2a-1) or 3^(b-1) must be 1 if 3 does not divide x, or y?

[patrickbriddon]

You say at 2:56 at k divides 3, but why does that then imply k=3? Could k=9 or 15 for example?