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ipynb/Beal.ipynb
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@ -29,11 +29,11 @@
"> <br>and $x, y, z$ are all greater than $2$, \n",
"> <br>then $A, B$ and $C$ must have a common prime factor.\n",
"\n",
"[Andrew Wiles](https://en.wikipedia.org/wiki/Andrew_Wiles) proved Fermat's theorem in 1995, but Beal's conjecture remains unproved, and Beal has offered [$1,000,000](http://www.ams.org/profession/prizes-awards/ams-supported/beal-prize) for a proof or disproof. I don't have the mathematical skills of Wiles, so I could never find a proof, but I can write a program to search for counterexamples. I first wrote [that program in 2000](http://norvig.com/beal2000.html), and [my name got associated](https://www.google.com/webhp?#q=beal conjecture) with Beal's Conjecture, which means I get a lot of emails with purported proofs or counterexamples (many asking how they can collect their prize money). So far, all the emails have been wrong. This notebook catalogs some of the more common errors, updates my 2000 program, and introduces this tool:\n",
"[Andrew Wiles](https://en.wikipedia.org/wiki/Andrew_Wiles) proved Fermat's theorem in 1995, but Beal's conjecture remains unproved, and Beal has offered [one million dollars](http://www.ams.org/profession/prizes-awards/ams-supported/beal-prize) for a proof or disproof. I don't have the mathematical skills of Wiles, so I could never find a proof, but I can write a program to search for counterexamples. I first wrote [that program in 2000](http://norvig.com/beal2000.html), and [my name got associated](https://www.google.com/webhp?#q=beal conjecture) with Beal's Conjecture, which means I get a lot of emails with purported proofs or counterexamples (many asking how they can collect their prize money). So far, all the emails have been wrong. This notebook catalogs some of the more common errors, updates my 2000 program, and introduces this tool:\n",
"\n",
"# Online Beal Counterexample Checker\n",
"\n",
"If you think you might have a valid counterexample, you should check it with my [Online Beal Counterexample Checker](http://norvig.com/bealcheck.html).\n",
"Got a counterexample? Check it with my **[Online Beal Counterexample Checker](http://norvig.com/bealcheck.html)**.\n",
"\n",
"# How to Not Win A Million Dollars\n",
"\n",
@ -197,7 +197,7 @@
"They say \"close\" only counts in horseshoes and hand grenades, and if you threw two horseshoes at a stake on **[Kapteyn-b](https://en.wikipedia.org/wiki/Kapteyn_b)** (an exoplanet 12.8 light years from Earth that is habitable and thus possibly horseshoe-playing) and the two paths differed in the 19th digit, the horseshoes would end up [less than an inch](https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=12.8%20light%20years%20*%201e-19%20in%20inches) apart. That's really, really close, but close doesn't count in number theory.\n",
"\n",
"![Kapteyn-b and Homer Simpson](https://norvig.com/homer.png)\n",
"<center>Left: [Kapteyn-b](https://www.space.com/26115-oldest-habitable-alien-planet-kapteyn-b.html). &nbsp; &nbsp; Right: [Homer Simpson](https://www.youtube.com/watch?time_continue=1&v=ReOQ300AcSU).</center>\n",
"Left: [Kapteyn-b](https://www.space.com/26115-oldest-habitable-alien-planet-kapteyn-b.html). &nbsp; &nbsp; Right: [Homer Simpson](https://www.youtube.com/watch?time_continue=1&v=ReOQ300AcSU).\n",
"\n",
"\n",
"# *The Simpsons* and Fermat\n",