Simplify Triplet: Redefining An in Terms of B & C

[chuck klasky]

I have been studying the Pythagorean theorem and Fermat’s Last theorem for fun and to brush up on my algebra.
I think I’ve come up with an equation for redefining An in terms of B and C. But my math is too rusty to verify if its correct.
I hope you look at it and see if there is a mistake somewhere. Thanks

C^n – B^n = A^n
C – B = Q so C/Q – B/Q = Q/Q =1.
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[C^n-B^n]/Q^n = C^n/Q^n – B^n/Q^n = (C/Q)^n- (B/Q)^n = (C/Q)^n – ((C-Q)/Q)^n
= (C/Q)^n – (C/Q – Q/Q)^n = (C/Q)^n – (C/Q -1)^n { C-B = Q }
= (C / C-B)^n – ( (C/ C-B) – 1)^n and so
[Cn-Bn]/(C-B)^n = (C / C-B)^n – ( (C/ C-B) – 1)^n and therefore
Cn-B^n = (C-B)^n [(C / C-B)^n – ( (C/ C-B) – 1)^n] = A^n

 

[MarkFL]

Hello Chuck!

I would highly recommend learning to typeset your work using $\LaTeX$...this makes the reading of math expressions much easier on the reader. We have tools present to aid users in the construction and previewing of their code as well. :D

 

[chuck klasky]

Sure-thanks. How? Where is the lesson plan?
chuck

 

[Jameson]

Sure-thanks. How? Where is the lesson plan?
chuck

Hi Chuck,

If you take a look at our http://mathhelpboards.com/latex-help-discussion-26/ then you can find some basic info but for this problem I'll try to give you some specific hints. :)

You can put equations between [MATH]...[/MATH] tags, or click the sigma sign you see in the toolbar when you are writing something.

For exponents, all you have to do is write them as you are already doing.

a^b becomes \(\displaystyle a^b\)

For fractions you make them like this:

\frac{a}{b} becomes \(\displaystyle \frac{a}{b}\)

Does that give you a start?

 

[CellCoree]

[(C / C-B)^n – ( (C/ C-B) – 1)^n]

Thank you for sharing your equation. It is an interesting approach to redefining An in terms of B and C. However, I would recommend double-checking your calculations and possibly using more familiar mathematical concepts and notations to make it easier to follow and verify. Additionally, it would be helpful to provide some context or explanation for your equation, as it is not immediately clear how it relates to the Pythagorean theorem or Fermat's Last theorem. Keep exploring and refining your ideas, and don't be afraid to seek feedback from other mathematicians.