Diophantine Fruit

[isaac21259]

https://thehighergeometer.wordpress.com/2021/07/27/diophantine-fruit/

[opheliate]

One of my favourite parodies of this "brain teaser" format invokes Fermat's last theorem: [0]

0: https://i.imgur.com/5QGR1Lt.jpeg

[kevinventullo]

To get a sense of how far one could push these fruit problems, see Matiyasevich’s Theorem (http://www.scholarpedia.org/article/Matiyasevich_theorem).

My understanding is a bit fuzzy, but it basically says you can encode any recursively enumerable set in terms of solutions to Diophantine equations (i.e. integer polynomials).

In particular you can encode, say, the set of all Turing Machines which halt in terms of the solutions to some integer polynomial.

[mjreacher]

See further discussion here: https://old.reddit.com/r/math/comments/osfc0x/you_know_those...

[londons_explore]

You need to add brackets...

The audience for these fruit problems don't 'do' typical multiplication-first arithmetic.

[technocratius]

Haha, great fun! The picture might need a few cycles of JPEG (re)compression to make it even more convincing.

[joshu]

delightfully cruel!