Waring's number mod m
نویسندگان
چکیده
منابع مشابه
The Fibonacci Sequence Mod m
We know that ( ) mod n F p forms a periodic sequence (vide Theorem 4). Let ( ) h p denote the length of the sequence. Let p be a prime such that: { } ( ) 2,3 mod 5 p ≡ a sufficient and necessary condition to ensure that ( ) 2 2 h p p + . We shall denote this group 1 G F . Let { } 1, 2 , , k D d d d = be the non-empty set of k divisors of 2 2 p + . Then for ( ) [ ] 1 min G i F h p d = such that ...
متن کاملLower Bounds for (MOD p - MOD m) Circuits
Modular gates are known to be immune for the random restriction techniques of Ajtai Ajt83], Furst, Saxe, Sipser FSS84], Yao Yao85] and H astad H as86]. We demonstrate here a random clustering technique which overcomes this diiculty and is capable to prove generalizations of several known modular circuit lower bounds of Barrington, Straubing, Th erien BST90], Krause and Pudll ak KP94], and other...
متن کاملSeparating the Communication Complexities of MOD m and MOD p Circuits
We prove in this paper that it is much harder to evaluate depth–2, size–N circuits with MOD m gates than with MOD p gates by k–party communication protocols: we show a k–party protocol which communicates O(1) bits to evaluate circuits with MOD p gates, while evaluating circuits with MOD m gates needs Ω(N) bits, where p denotes a prime, and m a composite, non-prime power number. As a corollary, ...
متن کاملThe ( mod , integral and exclusive ) sum number of graph
In this paper, we developed some new formulae for exclusive sum number of the complete bipartite graph , n m K . Also we show that for , 2 2 , 6 n n K E n K n 2 4, 2 6, 3 n n n and 2 4 n .
متن کاملMod-poisson Convergence in Probability and Number Theory
Building on earlier work introducing the notion of “modGaussian” convergence of sequences of random variables, which arises naturally in Random Matrix Theory and number theory, we discuss the analogue notion of “mod-Poisson” convergence. We show in particular how it occurs naturally in analytic number theory in the classical Erdős-Kac Theorem. In fact, this case reveals deep connections and ana...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2008
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2008.03.006