5 ms·
Diophantine Fruit
- joshu 5y agodelightfully cruel!
- opheliate 5y agoOne of my favourite parodies of this "brain teaser" format invokes Fermat's last theorem: [0] 0: https://i.imgur.com/5QGR1Lt.jpeg https://i.imgur.com/5QGR1Lt.jpeg
- mjreacher 5y agoSee further discussion here: https://old.reddit.com/r/math/comments/osfc0x/you_know_those_annoying_fruit_equation_memes/ https://old.reddit.com/r/math/comments/osfc0x/you_know_those...
- technocratius 5y agoHaha, great fun! The picture might need a few cycles of JPEG (re)compression to make it even more convincing.
- kevinventullo 5y agoTo get a sense of how far one could push these fruit problems, see Matiyasevich’s Theorem (http://www.scholarpedia.org/article/Matiyasevich_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.
- londons_explore 5y agoYou need to add brackets... The audience for these fruit problems don't 'do' typical multiplication-first arithmetic.
- john579 5y agox=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.