A very hard math riddle.

[south drift]

Idk how to solve it. I find it very hard.Idk if I can send this here too.

[valid harness]

@south drift this is an extremely difficult question whose solution involves the group of rational points on a specific elliptical curve. If you do not have a background in abstract algebra, then you will need quite a bit of work to understand the solution.

The original version of this meme was = 4 instead of = 10, and the smallest solution consists of 3 integers of around 80 digits each.

!elliptic curve meme

[barren crag]

🍎 = 154476802108746166441951315019919837485664325669565431700026634898253202035277999
🍌 = 36875131794129999827197811565225474825492979968971970996283137471637224634055579
🍍 = 4373612677928697257861252602371390152816537558161613618621437993378423467772036

[valid harness]

An explanation of the solution: https://ami.uni-eszterhazy.hu/uploads/papers/finalpdf/AMI_43_from29to41.pdf

Per the above, the solutions to the = 10 case are about 190 digits long

Best of luck!

[south drift]

Thx 🙂

[charred elk]

never knew there is a factoid for this 😭

[next pendant]

Is there no way to get the solution algebraically??

Like finding the GCD, then perhaps solving a polynomial, etc?

[charred elk]

elliptic curves is algebra, just abstract

[next pendant]

😔

[valid harness]

You can always solve diophantine equations algebraically. This is where the elliptic curve comes from.

The problem is finding integer solutions

[torpid aurora]

There are people with multiple math PHDs who, if they arent familiar with the fields involved (or dont have access to a sufficiently powerful computer) would not be able to answer this question for you.

[eager osprey]

Hmm....