Well, the last section wasn't. After you got a message on the e-mail account you made using TOR, you were asked a more complex mathematical question, and told not to tell anyone what it was, as they were tired of ircs and skype groups solving everything. I didn't realize I was one of the people selected to move on until a week later, though, and was too late to move forward.
You could at least entertain us with a real mathematical problem, even if not the one you were given, e.g. in how many ways can 54673350319220399841294938973353 be expressed as three times a square plus twice a (generalised) octagonal number. Bonus points for finding one set of explicit values.
Find integers a, b, c such that a^20 + b^20 = c^20. The solution turned out to be 4110^20 + 4693^20 = 4709^20. You can verify this is correct using any old calculator, for example:
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.
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.)
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
Wait a minute, is it somehow clear that you're supposed to be looking for a near-miss? If I came across this in my line of inquiry, I would assume that my previous step was wrong, and I'd have dropped the puzzle eventually.
Nah, I didn't actually do the Cicada 3301. I was just joking around. It seemed unlikely anyone was going to post an interesting math problem, so I decided to have a little fun. https://news.ycombinator.com/item?id=8549204
Fermat's last theorem has been proven; there is no solution, people. In this case, you can't verify this using "any old calculator," as most show only ten digits and these diverge at digit 12.
