Answer 8 and 9 only, make it computerize and ill give you thumbs up 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 alsoprime. 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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Answered: 8. Find the solutions to the given…

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8. Find the solutions to the given system of linear congruence. x= 1 (mod 3) x = 3 ( mod 5) x = 4 ( mod 7)

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter13: Sequences And Series

Section13.CT: Chapter Test

Problem 10CT

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Question

Answer 8 and 9 only, make it computerize and ill give you thumbs up

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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