Solve the linear congruence x3 – 7x² – 48x + 18 = 0 ( mod 54).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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ANS. number 10 only thank you
![1. Apply the Sieve Process from 200 to 300.
2. Let p be an odd prime not equal to 5. Prove that either p? – 1 or p? +1 is divisible by 10.
3. Prove that Vp is irrational for any prime p.
4. Let p, be the nth prime. Show by Mathematical Induction that Vn > 5, Pn > 2n – 1.
5. Numerical evidence makes it plausible that there are infinitely many primes p such that p+ 50 is also
prime. List 10 of these primes.
6. Find the remainder when 15 + 25 + 35 + ... + 985 + 995 + 1005 is divided by 4.
7. Without performing actual division, determine whether 1 010 908 899 is divisible by 7, 11 and 13.
8. Find the solutions to the given system of linear congruence.
x = 1 ( mod 3)
x = 3 ( mod 5)
x = 4 (mod 7)
9. Solve the linear congruence 17x = 9( mod 276) using systems of congruence.
10. Solve the linear congruence x3 – 7x² – 48x + 18 = 0 (mod 54).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff054445-f13f-4cb6-85a7-b39d780f58cd%2F70cdc129-dddd-47fe-b22c-7823d0836e35%2Fnnjizov_processed.png&w=3840&q=75)
Transcribed Image Text:1. Apply the Sieve Process from 200 to 300.
2. Let p be an odd prime not equal to 5. Prove that either p? – 1 or p? +1 is divisible by 10.
3. Prove that Vp is irrational for any prime p.
4. Let p, be the nth prime. Show by Mathematical Induction that Vn > 5, Pn > 2n – 1.
5. Numerical evidence makes it plausible that there are infinitely many primes p such that p+ 50 is also
prime. List 10 of these primes.
6. Find the remainder when 15 + 25 + 35 + ... + 985 + 995 + 1005 is divided by 4.
7. Without performing actual division, determine whether 1 010 908 899 is divisible by 7, 11 and 13.
8. Find the solutions to the given system of linear congruence.
x = 1 ( mod 3)
x = 3 ( mod 5)
x = 4 (mod 7)
9. Solve the linear congruence 17x = 9( mod 276) using systems of congruence.
10. Solve the linear congruence x3 – 7x² – 48x + 18 = 0 (mod 54).
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