Math Is Fun Forum

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Conjecture!

n³=a³+b³+c³
has no solutions. This is Euler's conjecture.
This was proved many years later by a counter example by another mathematician.
(I am sorry, I don't remember the numbers in the counter example. I shall make a note of it and post later)
The counter example had numbers all greater than a million. Later on, it was also proved that any number of solutions exist in the realm of numbers after that.
Where had the one eyed cyclops, the most gifted mathematician the planet had ever seen, gone wrong?
If I remember right, he had tested numbers only upto a million. Mathematics had shown us yet again that if something is true for every number up to a million, it is not necessarily true thereafter too.

(I had read this in the book FLT by Simon Singh.)

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Conjecture!

I have found

95800[sup]4[/sup] + 217519[sup]4[/sup] + 414560[sup]4[/sup] = 422481[sup]4[/sup]

At http://en.wikipedia.org/wiki/Euler%27s_sum_of_powers_conjecture

But nothing involving powers of 3

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Conjecture!

Euler also conjectured that Orthogonal Latin Squares don't exist for 4n + 6 for every n.  This is false, and while the counter example is not in the size of the millions, latin squares get very difficult to find for any number greater than 5 or so.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."