WebFIRST: (2^n)-1 IS ALLWAYS ODD - by definition one could say SECOND: NO, (2^4)-1 = 15 and this is NOT PRIME David Dean Studied at University of Oxford Author has 475 answers and 428.6K answer views 2 y Let [math]n = 11 [/math]. Then: [math]2^n -1 = 2^ {11} - 1 = 2047 = 23 \times 89. [/math] Therefore [math]2^n -1 [/math] is not always prime. WebShow that if 2n – 1 is prime then n must be prime. (Hint: You may wish to use the identity : for any a, b EN, 2ab – 1= (20 – 1) (24 (6-1) + 2a (6-2)... + 24 +1). This problem has been …
Prove the statements. There is an integer n such that
WebShow that if 2ⁿ − 1 is prime, then n is prime. Solution Verified Create an account to view solutions By signing up, you accept Quizlet's Recommended textbook solutions Discrete Mathematics and Its Applications 7th Edition Kenneth Rosen 4,285 solutions Discrete Mathematics 8th Edition Richard Johnsonbaugh 4,246 solutions Webodd, and use the condition φ(n) = n/2 to show that N = 1.] Solution: (i) If n is odd, then φ(2n) = φ(2)φ(n) = 1·φ(n) = φ(n). (ii) Suppose that n is an even integer, with n = 2km, where m is odd. Then φ(2n) = φ(2k+1m) = φ(2k+1)φ(m) = 2kφ(m) = 2(2k−1φ(m)) = 2φ(2km) = 2φ(n). (iii) Suppose that 3 - n. Then (3,n) = 1, and we have ... diluc white suit
Is it true that $2^n-1$ is prime whenever $n$ is prime?
WebDec 17, 2024 · How to prove that if 2^n - 1 is prime for some positive integer n, then n is also prime Tick, Boom! 728 subscribers Subscribe 11K views 2 years ago #math … WebWe would like to show you a description here but the site won’t allow us. WebExpert Answer Transcribed image text: 2. Prove or disprove the following statements: (a) If n is prime, then 3n-2n is prime. (b) If 3" - 2n is prime, then n is prime. (c) If m and n are both even and greater than two, then 3m- 2n is not a prime. Previous question Next question diluc with high ponytail