Is my solution for this gcd correct?

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Homework Help Overview

The discussion revolves around the correctness of a solution related to the greatest common divisor (gcd) of two functions, particularly focusing on the value -55/16 and its implications regarding coprimality.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning the origin of the value -55/16 and its relevance to the gcd. There is a discussion about the lack of rational zeroes for the function f(x) and the implications for factors with rational coefficients. Some participants are exploring the meaning of F5 and its relation to common factors.

Discussion Status

The discussion is ongoing, with participants expressing uncertainty about the calculations and interpretations. There is no explicit consensus, but there are points raised that suggest a need for clarification regarding the concepts of coprimality and the specific calculations involved.

Contextual Notes

Some participants mention previous steps that were removed from the discussion, indicating a dynamic exchange of ideas and interpretations. The context includes potential constraints related to the definitions of the functions and their properties in relation to the gcd.

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For the first part of this question:

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So if everything was done correctly is -55/16 my answer?
 
Last edited:
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-55/16 is a unit, so that is the same as saying they're co-prime
 
Maybe I'm missing something, but I don't get where the -55/16 comes from. f(x) has no zeroes in the rationals, hence no factors with rational coefficients.

I'm not sure what F5 means, but if it represents the integers modulo 5, both f and g have a common zero, hence a common factor.
 
Mark44 said:
Maybe I'm missing something, but I don't get where the -55/16 comes from. f(x) has no zeroes in the rationals, hence no factors with rational coefficients.

I'm not sure what F5 means, but if it represents the integers modulo 5, both f and g have a common zero, hence a common factor.

I had my solution steps up last night but I took it down after office_shredder made the point that it means they are coprime.
 
Last edited:
I'm still interested in where the -55/16 came from.
 
Last remainder of Euclidean division
 

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