Diophantine Fruit (thehighergeometer.wordpress.com)

delightfully cruel!

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

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

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

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

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.

You need to add brackets...

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

x=3,y=8,z=1 x=4,y=5,z=1 x=5,y=4,z=1 x=8,y=3,z=1 These are the only solutions.