Or a few bored guys on an IRC channel. A few websites, couple of phone numbers, and some posters: once you have members in the targeted cities, the budget for an operation like this is in tens of dollars.
> 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.
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.)
Google verifies the answer is 434437^15 + 588129^15 = 588544^15: https://www.google.com/search?q=434437%5E15+%2B+588129%5E15+...
> >>> 434437* * 15 + 588129* * 15 - 588544 * *15
(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.
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
Just because they don't disagree on the significant figures you can see doesn't mean there isn't a difference.
You might be interested to actually check out the actual problems, some of which have remained unsolved (at least by the general public) for years now.
Secret societies like that make my skin crawl.