
Homer's Last Theorem - leephillips
http://boingboing.net/2014/10/17/homers-last-theorem.html?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+boingboing%2FiBag+%28Boing+Boing%29
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ggchappell
This is a cute little easter egg.

However, it's actually not too hard to disprove 3987^12 + 4365^12 = 4472^12
with just a calculator. The thing to do is concern yourself with the rightmost
digits, not the leftmost.

The fake solution is actually a bit better than this article indicates, since
checking only the rightmost digit -- working modulo 10 -- doesn't show the
problem. 7^12 ends in 1, and 5^12 ends in 5. So the value of the left-hand
side of the proposed equation ends in 6. And so does 2^12.

But checking the rightmost 2 digits -- working modulo 100 -- we can see that
it doesn't work. 87^12 ends in 81, and 65^12 ends in 25. Their sum ends in 06.
But 72^12 ends in 16. So the proposed equation is false.

\-----

EDIT. For anyone who wonders how to do this.

Raising a number to the 3rd power, and then raising that to the 4th power, we
get the 12th power of the original number. If we are working modulo 100, then
we can throw out all but the rightmost 2 digits at any stage.

So, what are the rightmost 2 digits of 3987^12? Start by finding 87^3: 658503.
We only care about the "03" at the end. 03^4 = 81. So 3987^12 ends with 81.

Similarly, for 4365^12: 65^3 = 274625. 25^4 = 390625. So 4365^12 ends with 25.

And, for 4472^12: 72^3 = 373248. 48^4 = 5308416. So 4472^12 ends with 16.

81 + 25 = 106, which does not end with 16.

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Chinjut
Another simple disproof: 3987 and 4365 are both divisible by 3 (and thus so is
the left-hand side), but 4472 is not (and thus neither is the right-hand side,
as 3 is prime).

~~~
ggchappell
Very nice!

Another easy one is looking at it modulo 4. The powers on the left-hand side
are both odd perfect squares, which are thus 1 modulo 4. So their sum is 2
modulo 4. But the right-hand side is an even perfect square, which is 0 modulo
4.

EDIT. I guess my modulo-100 discussion is really just a convoluted way of
coming up with the above fact.

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Chinjut
So it turns out not only could we ignore all but the last digits of the
bases... we could furthermore ignore all but the last digits of the exponents!

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couchand
As an aficionado of both math and The Simpsons myself I quite liked the
author's book "The Simpsons and their Mathematical Secrets". One thing to note
before reading: it's targeted at an audience with a passing familiarity with
The Simpsons, so an unfortunate percentage of it is a description of episodes
you probably already know by heart. But it's a good read, anyway, so check it
out at your local library.

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ChrisBland
Another interesting easter egg is the Futurama Theorem
([http://theinfosphere.org/Futurama_theorem](http://theinfosphere.org/Futurama_theorem)).
The writers for some of these shows are brilliant people who happen to write
for cartoons.

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captaincrowbar
Obligatory xkcd link: [http://xkcd.com/217/](http://xkcd.com/217/)

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lskearney
Your theory of a donut-shaped universe intrigues me. I may have to steal it.

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gohrt
1\. How can anyone who cares that much about the Simpsons write "David S.
Cohen" _multiple_ times?

2\. Does anyone believe Fermat had a proof?

This article just smells sloppy.

~~~
neohaven
1\. You mean "David Samuel(S.) Cohen", one of the writers for The Simpsons and
Futurama, who decided to make his name "David X. Cohen" (not his legal name)
because the Writer's Guild does not accept duplicate names?

2\. Yes, people do believe he had a proof somewhere in his mind, considering
the rest of his track record. Whether that proof was correct is definitely up
for debate.

~~~
aaron695
> Whether that proof was correct is definitely up for debate.

No, no it's not.

You're not really understanding mathematics, which is fair enough, but also
the fundamentals of science and human nature with a statement like that.

~~~
neohaven
Fermat's Last Theorem is proven true, is it not?

Without having seen the proof that came to Fermat's mind, I don't think it's
anyone's absolute opinion on the matter that "It's not up for debate" and that
Fermat's proof being potentially true is "missing the fundamentals of
science".

If you may re-read my previous post, here's the thing people disagree on :
"Did Fermat write this having a correct proof of it on his mind or not?" I do
not think _anyone_ can say an absolute "yes" or "no" to this. Although it does
point to "no", considering that the mathematics used to prove FLT are far
beyond Fermat's time.

