Fermat´s Last theorem - book by Simon Singh

  • Context: Undergrad 
  • Thread starter Thread starter CAF123
  • Start date Start date
  • Tags Tags
    Book Theorem
Join the discussion
Ask a follow-up here, or get your own question answered by working scientists, mathematicians and engineers — people, not an autocomplete.
Real named experts · corrections over time · the nuance an AI answer skips
Sign up Log in
5 replies · 3K views
CAF123
Gold Member
Messages
2,918
Reaction score
87
I have been reading Fermat´s Last Theorem by Simon Singh and I noticed throughout he writes that the theorem states that there are no whole number solutions to x^n + y^n = z^n where n is greater than or equal to 3.
What about the trivial solns such as x =0, y=1 and z=1 etc?
Is this what the author means by no solutions, by ´not counting´these solns?
If so, I find it ironic that Singh continually makes the point that mathematics is a very precise subject and yet there is a small subtlety here.
Many thanks
 
Mathematics news on Phys.org
The key point is that, as you say, you need a whole number solution. Zero isn't a whole number, and so it can't be in a solution.
 
Mark M said:
The key point is that, as you say, you need a whole number solution. Zero isn't a whole number, and so it can't be in a solution.

Zero will be very disappointed to hear of its expulsion from the integers.

Of course "whole number" is ambiguous, referring variously to positive integers, nonnegative integers, and integers. FLT refers to positive integers, which resolves the OP's concern.
 
CAF123 said:
I have been reading Fermat´s Last Theorem by Simon Singh and I noticed throughout he writes that the theorem states that there are no whole number solutions to x^n + y^n = z^n where n is greater than or equal to 3.
What about the trivial solns such as x =0, y=1 and z=1 etc?
Is this what the author means by no solutions, by ´not counting´these solns?
If so, I find it ironic that Singh continually makes the point that mathematics is a very precise subject and yet there is a small subtlety here.
Many thanks


I was checking and yes: Singh comits the sin of lack of definition. In higher mathematics it is customary to state

FLT just like he does but with the understanding what we're talking about non-trivial solutions, which

are precisely the ones you mention. You can googloe FLT and find the correct statement in many sites, of course.

DonAntonio
 
SteveL27 said:
Zero will be very disappointed to hear of its expulsion from the integers.
-------------------------------------



It's a dwarf integer.


Dammit, why does it complain that my message is too short?
Here I'm trying to post a witty response and I have to put up with this crap. Dammit, still need 4 more characters. Oh wait, I just realizes, my message was too short - it's a dwarf reply!
 
What is happening?