A very interesting question

This is one of those deceptively hard questions. It is easy to figure out the answer, but it is nearly impossible to prove there are no other solutions! I thank Mateo for the suggestion! Special thanks this month to: Lee Redden, Mike Robertson, Daniel Lewis, Robert Zarnke, Kyle. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions 0:00 Problem 0:33 Answers 1:35 Solution part 1 6:18 Solution part 2 8:23 Solution part 3 Nick's Mathematical puzzles, #98 http://www.qbyte.org/puzzles/p098s.html Math StackExchange https://math.stackexchange.com/questions/571622/positive-integral-solutions-of-3x4y-5z/571668 Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay. Book ratings are from January 2022. My Books (worldwide links) https://mindyourdecisions.com/blog/my-books/#worldwide My Books (US links) Mind Your Decisions: Five Book Compilation https://amzn.to/2pbJ4wR A collection of 5 books: "The Joy of Game Theory" rated 4.2/5 stars on 224 reviews http://amzn.to/1uQvA20 "The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4/5 stars on 24 reviews http://amzn.to/1o3FaAg "40 Paradoxes in Logic, Probability, and Game Theory" rated 4.1/5 stars on 38 reviews http://amzn.to/1LOCI4U "The Best Mental Math Tricks" rated 4.2/5 stars on 76 reviews http://amzn.to/18maAdo "Multiply Numbers By Drawing Lines" rated 4.3/5 stars on 30 reviews http://amzn.to/XRm7M4 Mind Your Puzzles: Collection Of Volumes 1 To 3 https://amzn.to/2mMdrJr A collection of 3 books: "Math Puzzles Volume 1" rated 4.4/5 stars on 87 reviews http://amzn.to/1GhUUSH "Math Puzzles Volume 2" rated 4.1/5 stars on 24 reviews http://amzn.to/1NKbyCs "Math Puzzles Volume 3" rated 4.2/5 stars on 22 reviews http://amzn.to/1NKbGlp 2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter. My Blog https://mindyourdecisions.com/blog/ Twitter https://twitter.com/preshtalwalkar Merch https://teespring.com/stores/mind-your-decisions Patreon https://www.patreon.com/mindyourdecisions Press https://mindyourdecisions.com/blog/press