Let f(x) be a fixed integer polynomial, and let m be a fixed positive integer. Denote the number of solutions to f(x) = k (mod m) by N(k). Prove that m-1 EA ΣN(k) = k=0 ) = m.
Let f(x) be a fixed integer polynomial, and let m be a fixed positive integer. Denote the number of solutions to f(x) = k (mod m) by N(k). Prove that m-1 EA ΣN(k) = k=0 ) = m.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
[Algebraic Cryptography] How do you solve this?
Use the given hint: Let S(k) = {solutions to f(x) = (congruent to) k (mod m) in Z/mZ} where Z is the set of integers
Transcribed Image Text:Let f(x) be a fixed integer polynomial, and let m be a fixed positive integer. Denote the number of solutions to
f(x) = k (mod m) by N(k). Prove that
m-1
ΣN (k) =
k=0
= m.
Expert Solution
Step 1
This follows from basics of set theory. We give all the details in step 2.
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