Does anyone know the name for this equation?

Question

I have come across the following equation

a^n+b^n+c^n+......z^n=1

If you know all the other numbers this can be solved for n

Does anyone know what this equation is called , or even if it has a name, and if there are references to it on the internet.

Without a name I can't even Google for it :-(

Thanks for the tip. GMJB1960

It does not have 26 possible terms. It has an indefinite number but at least two..

I can't do subscripts on here to make it look correct.

Answer 1

For n=2 it is the k-dimensional sphere - x^2=1 the one dimensional sphere on the line {-1,1}, x^2+y^2=1 the two dimensional sphere in the plane i.e. a circle, x^2+y^2+z^2=1 a real 3D sphere, and so on through the dimensions. usually it reads |a|^n+|b|^n+...+|z|^n=1 so that for n=3, 4, 5, etc. the graph looks "sphere-ish". It is the Ln norm, well that raised to the n power, the Ln norm is ( |a|^n+|b|^n+...+|z|^n ) ^ (1/n). It is probably some other things also. See for instance http://mathworld.wolfram.com/VectorNorm.html

Answer 2

Don't know the name of the equation. Where did you come across it?

In any event, with n=1 there are a number of solutions.

Let a=1, b=-1, c=1 d= -1....w=1, x=-1, y= 2 z=-1
The above series gives 1 as the answer.

There is an infinite set of solutions as long n=1.

Answer 3

I san not imagine that this is some known equation.
If it where I am very sure that the mathematicien who studied this equations, would not limit the equation to 26 variables., He/she would mmake it general : a1^n + a2^n + .... ak^n=1

Answer 4

it is similar to fermat equation

Answer 5

it is similar to fermat equation