20. (a) Show that the sum of two odd prime numbers is never prime. (b) Is (a) true if the word odd is deleted?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 80E
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Q20

(d) Is the converse of (c) true? (If n is prime, need 2"-1
be prime?)
19. (a) [BB] Show that 26+1 is not prime.
(b) Show that 220 +1 is not prime.
(c) Show that if 2" +1 is prime then necessarily n is a
power of 2.
20. (a) Show that the sum of two odd prime numbers is
never prime.
(b) Is (a) true if the word odd is deleted?
21. [BB] Show that the sum of two consecutive primes is
never twice a prime.
22. If n is an odd integer, show that x2 - y² = 2n has no
integer solutions.
%3D
Transcribed Image Text:(d) Is the converse of (c) true? (If n is prime, need 2"-1 be prime?) 19. (a) [BB] Show that 26+1 is not prime. (b) Show that 220 +1 is not prime. (c) Show that if 2" +1 is prime then necessarily n is a power of 2. 20. (a) Show that the sum of two odd prime numbers is never prime. (b) Is (a) true if the word odd is deleted? 21. [BB] Show that the sum of two consecutive primes is never twice a prime. 22. If n is an odd integer, show that x2 - y² = 2n has no integer solutions. %3D
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