Fermat´s Last theorem - book by Simon Singh

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Discussion Overview

The discussion revolves around the interpretation of Fermat's Last Theorem as presented in Simon Singh's book, particularly regarding the definition of "whole number solutions" and the inclusion of trivial solutions such as (0, 1, 1).

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions whether Singh's assertion of no whole number solutions includes trivial solutions like (0, 1, 1), suggesting a potential lack of precision in Singh's definition.
  • Another participant clarifies that zero is not considered a whole number in the context of Fermat's Last Theorem, which refers specifically to positive integers.
  • A different participant notes the ambiguity of the term "whole number," indicating that it can refer to various definitions, and asserts that FLT is understood to refer to non-trivial solutions.
  • One participant humorously comments on the exclusion of zero from the integers, highlighting the informal nature of the discussion.
  • Another participant expresses frustration over the need for longer responses while attempting to make a witty remark.

Areas of Agreement / Disagreement

Participants express differing views on the definition of whole numbers and the inclusion of trivial solutions, indicating that there is no consensus on the interpretation of Singh's statement.

Contextual Notes

There is a lack of clarity regarding the definitions of "whole number" and "non-trivial solutions," which may affect the understanding of Fermat's Last Theorem as discussed in the thread.

CAF123
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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
 
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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?
 

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