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).

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).

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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