Does the equation x^{2}\equiv x*x\equiv 2x*4x \bmod 7 show that

Mary Reyes 2021-12-19 Answered
Does the equation x2xx2x4xbmod7 show that factorization of polynomials bmod7 is not unique? Why or why not?
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Expert Answer

Cassandra Ramirez
Answered 2021-12-20 Author has 30 answers
Step 1
x2xx2x4xbmod7
To show: factorization of polynomials bmod7 is not unique.
Other examples can be taken as
x23x5xbmod7
x26x6xbmod7
Step 2
From the above example it is clear that factorization of polynomials mod 7 is not unique as there are other factorization also.
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Orlando Paz
Answered 2021-12-21 Author has 42 answers
Step 1
Given that, the equation is x2xx2x4x(bmod7).
x2xx(bmod7)
x22x4x(bmod7)
From above equation, it is observed that the factorization of the polynomials (bmod7) is not unique.
Step 2
From above equation, it is observed that the factorization of the polynomials (bmod7) is not unique.
For example:
x22x4x(bmod7)
x2(24)(xx)(bmod7)
x2(35)(xx)(bmod7)
From above example, it is observed that the factorization of the polynomials (bmod7) is not unique.
Because, x21(bmod7) can have both solutions x±1(bmod7). That is, x1(bmod7) and x1(bmod7).
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