scholarly journals Simulated division with approximate factoring for the multiple recursive generator with both unrestricted multiplier and non-mersenne prime modulus

2003 ◽  
Vol 46 (8-9) ◽  
pp. 1173-1181 ◽  
Author(s):  
Hui-Chin Tang
Keyword(s):  
Multiple Recursive Generator ◽  
Prime Modulus ◽  
Mersenne Prime

Pseudoperfect numbers with no small prime divisors

2009 ◽  
Vol 93 (528) ◽  
pp. 404-409
Author(s):  
Peter Shiu
Keyword(s):  
Difficult Problem ◽  
Prime Divisors ◽  
Perfect Number ◽  
Perfect Numbers ◽  
Mersenne Primes ◽  
Mersenne Prime

A perfect number is a number which is the sum of all its divisors except itself, the smallest such number being 6. By results due to Euclid and Euler, all the even perfect numbers are of the form 2P-1(2p - 1) where p and 2p - 1 are primes; the latter one is called a Mersenne prime. Whether there are infinitely many Mersenne primes is a notoriously difficult problem, as is the problem of whether there is an odd perfect number.

Fast mersenne-prime transforms for digital filters

1979 ◽  
Vol 126 (2) ◽  
pp. 203
Author(s):  
R.L. Miller ◽  
I.S. Reed ◽  
T.K. Truong
Keyword(s):  
Digital Filters ◽  
Mersenne Prime

scholarly journals Pairs of additive congruences to a large prime modulus

1989 ◽  
Vol 46 (3) ◽  
pp. 438-455 ◽  
Author(s):  
O. D. Atkinson ◽  
R. J. Cook
Keyword(s):  
Trivial Solution ◽  
Prime Modulus ◽  
Image Position

AbstractThis paper is concerned with non-trivial solvability in p–adic integers, for relatively large primes p, of a pair of additive equations of degree k > 1: where the coefficients a1,…, an, b1,…, bn are rational integers.Our first theorem shows that the above equations have a non-trivial solution in p–adic integers if n > 4k and p > k6. The condition on n is best possible.The later part of the paper obtains further information for the particular case k = 5. specifically we show that when k = 5 the above equations have a non-trivial solution in p–adic integers (a) for all p > 3061 if n ≥ 21; (b) for all p execpt p = 5, 11 if n ≥ 26.

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