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Am I missing something, doesn't this contradict Fermat's last theorem > In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especial
by dil8 12y ago
Am I missing something, doesn't this contradict Fermat's last theorem
> In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than two.
https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem
- TheLoneWolfling 12y agoYou're not missing anything. His numbers do not add up to the same thing. In other words, 4709^20 != (4110^20 + 4693^20). (The difference is ~10^61 or so, whereas the numbers are ~10^73. In other words, they diverge at ~ the 12th digit, whereas many calculators only display 10.)
- sillysaurus3 12y agoHm, well, part 2 of the question was to find a solution for a^15 + b^15 = c^15, where a, b, c are integers > 0. Google verifies the answer is 434437^15 + 588129^15 = 588544^15: https://www.google.com/search?q=434437%5E15+%2B+588129%5E15+-+588544%5E15 https://www.google.com/search?q=434437%5E15+%2B+588129%5E15+...
- TheLoneWolfling 12y agoNope. This is not correct either. > >>> 434437* * 15 + 588129* * 15 - 588544 * *15 > -604550152144288043930860169354171954730939671404246170822386878582482 (Edit: how do I display two asterisks in a row? It's supposed to be number(asterisk)(asterisk)number.) This is using Python, which does arbitrary-precision integer arithmetic. Google's calculator probably uses floating-point numbers internally, and hence starts losing precision.
- sillysaurus3 12y agoIt seems that advancements in technology have made mathematical trolling much more difficult. :) In case anyone is curious, the above "solutions" are called near-misses, since they're almost correct. A clever person came up with an algorithm to generate interesting near-misses for low exponents. See the table on page 15: http://arxiv.org/pdf/math/0005139v1.pdf http://arxiv.org/pdf/math/0005139v1.pdf Related: http://math.stackexchange.com/questions/526330/fermats-last-theorem-near-misses http://math.stackexchange.com/questions/526330/fermats-last-... Have fun!
- TheLoneWolfling 12y agoPython having easy arbitrary-precision integer arithmetic is one of the things I most like about it.
- wbhart 12y agoWhat you really need is a "solution" that is wrong in just one digit somewhere in the middle that everyone would easily miss when comparing.
- yen223 12y agoArbitrary-precision integers is definitely one of Python's underrated feature.
- dil8 12y agoWell according the the theorem there is no integer solutions when the exponent is greater than 2.
- TheLoneWolfling 12y agoHis counterexample is incorrect.