20. (a) Show that the sum of two odd prime numbers is never prime. (b) Is (a) true if the word odd is deleted?
20. (a) Show that the sum of two odd prime numbers is never prime. (b) Is (a) true if the word odd is deleted?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe8861517-a105-41fe-a838-ce7abed98fce%2F03d33bf8-c187-4e77-9704-41c4ecac18ba%2F48c1fa.jpeg&w=3840&q=75)
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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