(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...

Q20

Extracted 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