Math Is Fun Forum

Prakash Panneer

Member

Registered: 2006-06-01

Posts: 110

Number

Is there any number which satisfy a^3+b^3=c^3?

Where a,b,c are not equal to 0.

Thanks in advance.

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chemhelper

Member

Registered: 2007-01-09

Posts: 2

Re: Number

Please give more details about your question.  When you say number, do you mean a number such that a=b=c?  Must a,b,c have the same values or can they be different.

Last edited by chemhelper (2007-01-10 10:52:51)

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Number

If chemhelper's assumption that a=b=c is correct, then there are clearly no answers, because the equation would become 2a³ = a³, and we're already told that the numbers are non-zero.

If they all have to be integers, then Fermat's Last Theorem says that there are no answers. If they are allowed to be non-integer, then there are infinite solutions. You can pick any a and b and there will always be a value for c (unless a =-b, in which case c would have to be 0).

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