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 [quote="Bicho the Inhaler"]"There are no coincidences in the natural numbers." or something to that effect, said by someone or other famous.[/quote]
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dave10000
Posted: Sun Mar 10, 2002 5:06 am    Post subject: 1

For no good reason, I wrote the following Mathematica program:

While[
(a = Random[Integer, {1000, 1500}]) ||
(b = Random[Integer, {1000, 1500}]) ||
(c = Random[Integer, {1000, 1500}]) ||
!IntegerQ[(a^3 + b^3 + c^3)^(1/3)]]
Print[a]
Print[b]
Print[c]
Print[(a^3 + b^3 + c^3)^(1/3)]

In under 2 minutes of run time, my computer told me that:

1004^3 + 1219^3 + 1332^3 = 1731^3
Coyote
Posted: Sat Mar 09, 2002 10:37 pm    Post subject: 0

http://mathforum.org/dr.math/problems/toscano7.14.97.html

I don't really understand why Fermat's Last Theorem being proven implies that no formula for finding solutions to a^3+b^3+c^3=d^3 exists, but if it's true, I doubt there'll be any 'practical' application similar to the Pythagorean Theory.

The article lists several other solutions to the equation though, just in case anyone wants to look them over and try to figure out some kind of connecting idea to them.
Bicho the Inhaler
Posted: Sat Mar 09, 2002 6:19 pm    Post subject: -1

Yes, page 398 of Hoftstadter's GEB. That must have been it.
Suspence
Posted: Sat Mar 09, 2002 3:05 pm    Post subject: -2

I found the quote to which Mr. Inhaler refers:

"Achilles: An "infinite coincidence"? Among the natural numbers, NOTHING is coincidental-nothing happens without there being some underlying pattern. "

It has to mean something somewhere...but what???

------------------
I hate people who try to write interesting things in their signature
groza528
Posted: Sat Mar 09, 2002 7:31 am    Post subject: -3

Not that I know of (displays title)
Lepton
Posted: Sat Mar 09, 2002 4:36 am    Post subject: -4

But no funky trigangle-y goodness?
daniel801
Posted: Fri Mar 08, 2002 6:51 pm    Post subject: -5

...if re-frozen
daniel801
Posted: Fri Mar 08, 2002 5:12 pm    Post subject: -6

it means that three ice cubes of sides 3, 4, and 5 when melted would fit in an ice cube tray with side 6
Bicho the Inhaler
Posted: Fri Mar 08, 2002 4:59 am    Post subject: -7

"There are no coincidences in the natural numbers." or something to that effect, said by someone or other famous.
Chuck
Posted: Fri Mar 08, 2002 4:54 am    Post subject: -8

Mere coincidence. It means nothing.
Lepton
Posted: Fri Mar 08, 2002 4:09 am    Post subject: -9

a^2 + b^2 = c^2
3^2 + 4^2 = 5^2
.......Everyone knows Pythagores' Theorem.

a^3 + b^3 + c^3 = d^3
3^3 + 4^3 + 5^3 = 6^3
........Fancy, eh?

What does d^3 signify?
(I don't know the answer myself)