If you don’t want to tell us precisely what your conjecture is, then there’s no point having any discussion…
Have you ever seen an equation that sets restrictions on how many numbers with exponents are needed to reach another number with the same exponent?
What do you mean by “expansion”?
It seems like you’re just talking about basic Diophantine equations. Here’s a description of 2nd power Diophantine equations. A related equation that is quite familiar to number theory students is Pell’s equation. Perhaps you’ve run into it?
Similar “expansions” were studied before, during, and after Fermat’s time. They were, after all, all specific forms of a type of equation posed by Diophantus several centuries earlier.
No it is very different.
the theory i have I think (and this is my opinion) a lot more complex
The equation Im thinking of has an unlimited number of terms
No need to multi-post. Just stated the darned theorem and have done with it. No need to be coy. Otherwise, there’s no point in you posting anything in this thread at all.
x^n=w1^n+w2^n+w3^n+ . . . wn-p^n
p> or p= 0
has anyone here seen that before or have an example where i’m wrong?
What is your conjecture? That there is an integer solution of x for every n? Or something else?
yep as long as n is natural number greater than 1.
suddenly you all stop saying it isn’t original
So, if I have this correctly, you’re saying there’s a way (in positive integers) to express a sum of m many nth powers as an nth power, whenever m <= n?
if n>1 and p=0 or is p>0 x always has a positive, real,ration,whole answer
Real, rational, or whole? Those are three different things.
nope if it is whole it is rational and real.
I assume they mean (redundantly) all three.
I don’t know why they leave out n = 1, when that case is trivially possible as well…
23 =15+16
that two terms and the power is one therefore it doesn’t. Only from 2.
How brilliant am I