What is the identity of a3 + b3 + c3 in math?

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Homework Help Overview

The discussion revolves around the mathematical expression a³ + b³ + c³ and the inquiry into whether it represents an identity. Participants express confusion regarding the nature of the expression and its classification as an identity.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Some participants question the definition of an identity and whether the expression qualifies as one. Others explore the implications of the expression being a sum of cubes and its relation to known mathematical theorems.

Discussion Status

The discussion is ongoing, with participants clarifying the distinction between expressions and identities. There is a recognition of the need to define terms more clearly, and some participants are exploring the implications of the expression in the context of established mathematical principles.

Contextual Notes

There is a mention of Fermat's Last Theorem, which introduces constraints on the values of a, b, and c if they are considered as positive integers.

phymatter
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Homework Statement


what is the identity of a3 + b3 + c3
i am getting a bit confused please help!


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The Attempt at a Solution

 
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phymatter said:

Homework Statement


what is the identity of a3 + b3 + c3
i am getting a bit confused please help!
I don't know what you are asking. An identity is an equation that is always true. What you have isn't an equation, so can't be an identity.

If you are asking is there some identity that involves the sum of three cubes, I don't recall seeing one like that.
 


Are a, b, and c arbitrary integers?
 


First off, what you wrote out is no identity or an equation, this is an expression. Secondly, if it were to be like this:

a3+b3=c3It would still be impossible if a, b, and c were 3 positive integers based on Fermat's Last Theorem.
 

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