# Expended Fermats last theorem

#### robert80

You all know that the Fermats last theorem is solved for some years and that the equation

a^n + b^n = c^n

is solved when a,b,c being the natural numbers only for n = 2.

I would like to expand a problem:

Can anybody proove that:

a^n + b^n + c^n = d^n has a solutions a,b,c,d in the natural numbers for n = 3 and that for each higher n equation is non solveable?

Lets carry on: Can anybody proove that a^n + b^n + c^n + d^n + e^n = f^n for n = 4 the last solution exists?and for n>4 there are no solutions?

Thanks,

Robert

it would be very nice to find the rule, how many particles on the power of n you have to sum that you get the last solution of the equation in order of given n.

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#### D H

Staff Emeritus
You appear to be asking about Euler's conjecture, which is now known to be false.

958004 + 2175194 + 4145604 = 4224814
275 + 845 + 1105 + 1335 = 1445

#### robert80

So you need at least n-1 natural numbers in order to define next one ? I dont know anything about Eulers conjecture...I dont even know it exists :)

#### robert80

Sorry now I see, havent heard about it before. I have read it on Wikipedia now. But its funny that I got the idea without hearing f it :) Just some centuries too late :)

#### robert80

Just one more thing. Does this holds for any n? How can we know or assume, how many variables we need in order to describe a next one?Isnt it possible that when we reach n = 1000 we need much more variables (or less) than when n = 999? Does it have any importance in some special vector spaces? Thank you.

Staff Emeritus