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

Click For Summary
SUMMARY

The expression a³ + b³ + c³ does not represent an identity in mathematics, as it is not an equation that holds true universally. An identity is defined as an equation that is always valid, while a³ + b³ + c³ is merely an expression. Furthermore, the discussion highlights that if a, b, and c are positive integers, the equation a³ + b³ = c³ cannot be satisfied, in accordance with Fermat's Last Theorem.

PREREQUISITES
  • Understanding of algebraic expressions and identities
  • Familiarity with Fermat's Last Theorem
  • Basic knowledge of integer properties
  • Concept of mathematical equations versus expressions
NEXT STEPS
  • Research the properties of algebraic identities
  • Study Fermat's Last Theorem in detail
  • Explore the sum of cubes formula and its implications
  • Learn about mathematical expressions versus equations
USEFUL FOR

Students studying algebra, mathematicians exploring number theory, and educators teaching mathematical identities and expressions.

phymatter
Messages
131
Reaction score
0

Homework Statement


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


Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org


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.
 

Similar threads

Simplifying expression with vectors
  • · Replies 14 ·
Replies
14
Views
3K
Finding values to make a linear system consistent
  • · Replies 6 ·
Replies
6
Views
5K
Constructing a 3x3 Linear system question
  • · Replies 4 ·
Replies
4
Views
2K
How Do You Solve a System with Variables and Constants?
  • · Replies 7 ·
Replies
7
Views
2K
Comp Sci An Introduction to Deep Learning and Modifying Code
  • · Replies 7 ·
Replies
7
Views
2K
(x-y)3 + (y-z)3 + (z-y)3 = 3(x-y)(y-z)(z-x)
  • · Replies 4 ·
Replies
4
Views
16K
Proof of Partition of a Set with Nested Partitions | Set Theory Proof 2
  • · Replies 5 ·
Replies
5
Views
2K
Trig Identities -- example problem confusion
  • · Replies 10 ·
Replies
10
Views
2K
Prove the identity matrix is unique
  • · Replies 69 ·
3
Replies
69
Views
9K
Find the scalar, vector, and parametric equations of a plane
  • · Replies 10 ·
Replies
10
Views
3K