Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Oxford University Press, Oxford, 1960. 【3】Another elementary proof that p(11n+6)≡0 (mod 11). Syrous Marivani. 【4】Distribution of the Partition Function Modulo m. Ken Ono....
s theorem [16, Chapter 8], Waring type formulas [12], distribution of rationalnumbers in short intervals [9], equipartition modulo odd integers [2], large sieve inequality [20], aswell as other areas of mathematics.Ramanujan sums have been generalized by many mathematicians in several contexts...
sum of squaressum of triangular numbersFor positive integers [Formula: see text], [Formula: see text] and [Formula: see text], let [Formula: see text] denote the number of representations of a nonnegative integer [Formula: see text] as [Formula: see text] where [Formula: see text], ...
You haveNintegers,A1,A2, ... ,AN. You need to deal with two kinds of operations. One type of operation is to add some given number to each number in a given interval. The other is to ask for the sum of numbers in a given interval. Input The first line contains two numbersNandQ....
Ramanujan’s chief contribution to mathematics was his work in number theory. This area of mathematics is concerned with the properties of numbers, and Ramanujan developed a number of new results in this field. He also made important contributions to other areas of mathematics, including combinatoric...
We obtain asymptotic formulas for the sums $$\\sum_{... TH Chan,AV Kumchev - 《Eprint Arxiv》 被引量: 20发表: 2012年 Distribution of averages of Ramanujan sums The average value of a certain normalization of Ramanujan sums is determined in terms of Bernoulli numbers and odd values of...
M(x)<\sum_{n\le x}{(a_n-b_n)^2\over c_n^2}\tag6 如果能够证明最右侧在x增大时为o(x),就能在a_n和b_n之间建立伪渐近关系了。下面我们就来通过这种办法来探讨\omega(n)和\log\log n之间的伪渐近关系。 方差的估计 利用完全平方公式,可知: ...
After a short recall of the basic asymptotic relations "big O" and "small o", we consider the Cauchy sums of the form \\\(\\\displaystyle \\\sum _{a\\\le k0\\\); in the case where \\\(\\\alpha =1\\\) these are strictly related to the celebrated Riemann sums. After having...
One of the first users of BIT's new supercomputer was Chip Diller. He extended his exploration of powers of 3 to go from 0 to 333 and he explored taking various sums of those numbers. ``This supercomputer is great,'' remarked Chip. ``I only wish Timothy were here to see these result...
This program finds all the numbers within the max limit entered by the user, that can be written as sum of cubes of two different numbers in two different ways. the program will prompt for max value where you've to give the max range of all the four different numbers. note: the...