Trace representation of Legendre sequences of Mersenne prime period

1996 ◽  
Vol 42 (6) ◽  
pp. 2254-2255 ◽  
Author(s):  
Jong-Seon No ◽  
Hwan-Keun Lee ◽  
Habong Chung ◽  
Hong-Yeop Song ◽  
Kyeongcheol Yang
Keyword(s):  
Prime Period ◽  
Trace Representation ◽  
Mersenne Prime

A Simpler Trace Representation of Legendre Sequences

2015 ◽  
Vol E98.A (4) ◽  
pp. 1026-1031 ◽  
Author(s):  
Minglong QI ◽  
Shengwu XIONG ◽  
Jingling YUAN ◽  
Wenbi RAO ◽  
Luo ZHONG
Keyword(s):  
Trace Representation

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.

Trace Representation and Linear Complexity of Binary $e$th Power Residue Sequences of Period $p$

2011 ◽  
Vol 57 (3) ◽  
pp. 1530-1547 ◽  
Author(s):  
Zongduo Dai ◽  
Guang Gong ◽  
Hong-Yeop Song ◽  
Dingfeng Ye
Keyword(s):  
Linear Complexity ◽  
Trace Representation
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