A conjecture on composite terms in sequence generated
... up with an infinite sequence 2, M2, MM2, MMM2, MMMM2. MMMMM2,…, which are generated from recurrence relations and called Catalan-Mersenne numbers. Are these numbers all prime? It has been an unsolved problem[2,3,4,5], because in Catalan-Mersenne number sequence the first five terms 2, M2, M3, M7, M1 ...
... up with an infinite sequence 2, M2, MM2, MMM2, MMMM2. MMMMM2,…, which are generated from recurrence relations and called Catalan-Mersenne numbers. Are these numbers all prime? It has been an unsolved problem[2,3,4,5], because in Catalan-Mersenne number sequence the first five terms 2, M2, M3, M7, M1 ...
New Generalized Cyclotomy and Its Applications
... Cyclotomy is an old topic of elementary number theory. Cyclotomic and generalized cyclotomic numbers are related to Waring’s problem [6], difference sets [3, 16, 17], sequences [4, 5, 10], coding theory [14, 15], and cryptography [7]. Classical cyclotomy was dealt to a good extent by Gauss in his ‘‘ ...
... Cyclotomy is an old topic of elementary number theory. Cyclotomic and generalized cyclotomic numbers are related to Waring’s problem [6], difference sets [3, 16, 17], sequences [4, 5, 10], coding theory [14, 15], and cryptography [7]. Classical cyclotomy was dealt to a good extent by Gauss in his ‘‘ ...
1 (1 mark) (1 mark) (2 marks) (3 marks) (2 marks) (4 marks) (2 marks
... Let a, b, c be integers such that a|bc and (a, b) = 1. Use the existence of integers s and t satisfying sa + tb = 1 to show that a|c. (3 marks) ...
... Let a, b, c be integers such that a|bc and (a, b) = 1. Use the existence of integers s and t satisfying sa + tb = 1 to show that a|c. (3 marks) ...
Fibonacci Pitch Sequences: Beyond Mod 12
... residue 6, and l1 is missing residues 0 and 9. The impact of the defective modulus is heightened in mod 24. Table 3 shows the number of occurrences of each residue class in prime sequences. f1 generates the set of pitches {0, 1, 2, 3, 5, 7, 8, 10, 13, 16, 17, 21, 23}. Multiply this by five and we ge ...
... residue 6, and l1 is missing residues 0 and 9. The impact of the defective modulus is heightened in mod 24. Table 3 shows the number of occurrences of each residue class in prime sequences. f1 generates the set of pitches {0, 1, 2, 3, 5, 7, 8, 10, 13, 16, 17, 21, 23}. Multiply this by five and we ge ...
Mod p - Math.utah.edu
... The other numbers: 2, 6, 7, 8, 10 have no square roots. Exercise 2. Continue this for the primes p = 13, 17, 19, 23 and 29. Remember that with the real numbers, the discriminant b2 − 4ac has two square roots if it is positive and none if it is negative. Unfortunately, in mod p algebra, we have nothi ...
... The other numbers: 2, 6, 7, 8, 10 have no square roots. Exercise 2. Continue this for the primes p = 13, 17, 19, 23 and 29. Remember that with the real numbers, the discriminant b2 − 4ac has two square roots if it is positive and none if it is negative. Unfortunately, in mod p algebra, we have nothi ...
Document
... exponentiation algorithm, 0981937 mod 2537 = 0704 and 0461937 mod 2537 = 1115. Consequently, the numerical version of the original message is 0704 1115. Translating this back to English letters, we see that the massage is HELP. In summary, given 2 large prime numbers p and q (usually more than 200 d ...
... exponentiation algorithm, 0981937 mod 2537 = 0704 and 0461937 mod 2537 = 1115. Consequently, the numerical version of the original message is 0704 1115. Translating this back to English letters, we see that the massage is HELP. In summary, given 2 large prime numbers p and q (usually more than 200 d ...
