How many distinct degree 7 polynomials are there over the modular arithmeic modulo 7?

django0a6

django0a6

Answered question

2022-11-20

How many distinct degree 7 polynomials are there over the modular arithmeic modulo 7?
If it's infinite, is it countable or uncountable infinite?
I am a newbie to this topic... I don't know what modular arithmetic for polynomials means. Can someone please give me a link where I can learn?

Answer & Explanation

Claudia Woods

Claudia Woods

Beginner2022-11-21Added 15 answers

Step 1
There are 8 coefficients to be determined.
Step 2
The lead coefficient cannot be 0. So the number is ( 6 ) ( 7 7 ).
trumansoftjf0

trumansoftjf0

Beginner2022-11-22Added 5 answers

Step 1
All such polynomials look like:
a 1 x 0 + a 2 x 1 + + a n x n 1 + a n + 1 x n
where a i { 0 , 1 , , n 1 } for 1 i n and a n + 1 { 1 , 2 , , n 1 } .
Step 2
So there are
n × n × × n n  times × ( n 1 ) = n n × ( n 1 )
such polynomials.

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