[TheLoneWolfling]

You'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]

Hm, 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+...

[TheLoneWolfling]

Nope. 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]

It 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

Related: http://math.stackexchange.com/questions/526330/fermats-last-...

Have fun!

[wbhart]

What you really need is a "solution" that is wrong in just one digit somewhere in the middle that everyone would easily miss when comparing.

[TheLoneWolfling]

Python having easy arbitrary-precision integer arithmetic is one of the things I most like about it.

[yen223]

Arbitrary-precision integers is definitely one of Python's underrated feature.

[dil8]

Well according the the theorem there is no integer solutions when the exponent is greater than 2.

[TheLoneWolfling]

His counterexample is incorrect.