Q5. (a) (b) Let P1 and P2 be distinct odd primes such that (p₁ − 1) | (p2 − 1). Let m = P1P2. Prove that the equation [x]²² + [x] − [1] = [0] has a unique solution in Zm. - (0) bas a Find an integer xo, with 0 ≤ xo

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 51RE
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Q5.
(a)
(b)
Let p₁ and p2 be distinct odd primes such that (p₁-1) | (p2-1). Let m = pip2.
Prove that the equation [x]P² + [x] – [1] = [0] has a unique solution in Zm.
has L
P2
Find an integer xo, with 0 ≤ xo <m, such that [ro]⁹² + [xo] − [1] = [0] in Zm.
Note: Your value of xo will depend on the value of m.
Transcribed Image Text:Q5. (a) (b) Let p₁ and p2 be distinct odd primes such that (p₁-1) | (p2-1). Let m = pip2. Prove that the equation [x]P² + [x] – [1] = [0] has a unique solution in Zm. has L P2 Find an integer xo, with 0 ≤ xo <m, such that [ro]⁹² + [xo] − [1] = [0] in Zm. Note: Your value of xo will depend on the value of m.
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