[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 Let f(x) be a fixed integer polynomial, and let m be a fixed positive integer. Denote the number of solutions tof(x) = k (mod m) by N(k). Prove thatm-1ΣN (k) =k=0= m.

Answered: Let f(x) be a fixed integer polynomial,…

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

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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