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#1 2009-01-13 19:06:40
- Jai Ganesh
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An interesting equation!
By chance, it occured to me
where a=1, b=2, c=3, d=4, and e=5.
Can any of you think of why this may not be the only solution to the equation? I think it is a unique solution since the values of cubes of numbers grow at a much more rapid rate than the squares.
Views/Comments please.
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.
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#2 2009-01-14 00:58:11
- JaneFairfax
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Re: An interesting equation!
Presumably you mean are all positive integers.
Well, I found another solution:
Last edited by JaneFairfax (2009-01-14 02:16:15)
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#3 2009-01-14 01:05:04
- Ricky
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Re: An interesting equation!
SOSASOC (squares of sums and sums of cubes)
This is an old problem (18th century maybe?), and new results have been published on it recently. If you work out the induction, you'll find that (1, ..., n) is always a solution. Given a number n, (d_1, d_2, ..., d_n) where each d_i is the number of divisors of a divisor of n is also a solution. There is also a way to multiply to solutions together to find a new third solution. Under a certain mapping, all solutions can be viewed as the kernel of a homomorphism from a direct sum of integers to the rationals.
This link has some of these results, and is an easy read, perhaps even those without much of a mathematical background.
"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..."
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#4 2009-01-14 01:12:25
- JaneFairfax
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Re: An interesting equation!
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#5 2009-01-14 02:12:06
- Jai Ganesh
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Re: An interesting equation!
Thanks Ricky, for that link. It seems pretty interesting.
Thanks Jane, for taking the trouble of finding alternate solutions. You always manage to find a flaw in what I do, ha! 
Just kiddin'.
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.
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#6 2009-01-14 14:53:31
- JaneFairfax
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Re: An interesting equation!
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#7 2009-01-14 17:57:30
- Jai Ganesh
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- Registered: 2005-06-28
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Re: An interesting equation!
Maybe I should've added
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.
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