Don't try this puzzle

It looks childish, but this puzzle is sadistically difficult. Saying that 95% of people can't solve this is like saying 95% of people can't jump over a skyscraper.

Here is the simplest solution:

apple = 154476802108746166441951315019919837485664325669565431700026634898253202035277999

banana =
36875131794129999827197811565225474825492979968971970996283137471637224634055579

pineapple =
4373612677928697257861252602371390152816537558161613618621437993378423467772036

You need a serious course on number theory to learn how to solve this. So it's easier than jumping over a skyscraper: you can learn to do it. But without some education, it's pretty much impossible.

The trick is to transform the equation into an elliptic curve. An elliptic curve is a kind of curve whose points form a group. That means if you find one point on the curve, you can find more. So if you can find one solution of this puzzle, you can find more.

Umm, but then you still need to find a solution! Luckily there's a small solution where the variables are integers that aren't positive:

apple = 4

banana = -1

pineapple = 11

From this you can turn the crank and get more solutions, but they get bigger and bigger, and the first one where all three variables are positive is the one I showed you.

I got all this from a wonderful Quora post by Alon Amit:

https://www.quora.com/How-do-you-find-the-integer-solutions-to-frac-x-y+z-+-frac-y-z+x-+-frac-z-x+y-4/answer/Alon-Amit

but I heard about that from +David Eppstein, here on G+. So: add David Eppstein to your list of cool people you follow on G+!

The post by Alon Amit is worth reading, because he leads you through the number theory without getting too technical (leaving out lots of juicy details that you'd get in a course on elliptic curves), and he gives some examples of similar problems that are much harder - if you don't know the trick.

#bigness
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