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In number theory, a narcissistic number [1] [2] (also known as a pluperfect digital invariant (PPDI), [3] an Armstrong number [4] (after Michael F. Armstrong) [5] or a plus perfect number) [6] in a given number base is a number that is the sum of its own digits each raised to the power of the number of digits.
This is a list of recreational number theory topics (see number theory, recreational mathematics). Listing here is not pejorative : many famous topics in number theory have origins in challenging problems posed purely for their own sake.
This function arises in more precise analyses of the algorithms mentioned above, and gives a more refined time bound. In the disjoint-set data structure, m represents the number of operations while n represents the number of elements; in the minimum spanning tree algorithm, m represents the number of edges while n represents the number of vertices.
The authors provide a GitHub repository with implementations of various exercises and algorithms from the book in different programming languages. [ 7 ] [ 8 ] Programs in the book are presented in pseudo code with implementations in Java , Python , Lisp , JavaScript , and Scala available online.
In number theory and computer science, the partition problem, or number partitioning, [1] is the task of deciding whether a given multiset S of positive integers can be partitioned into two subsets S 1 and S 2 such that the sum of the numbers in S 1 equals the sum of the numbers in S 2.
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A prime divides if and only if p is congruent to ±1 modulo 5, and p divides + if and only if it is congruent to ±2 modulo 5. (For p = 5, F 5 = 5 so 5 divides F 5) . Fibonacci numbers that have a prime index p do not share any common divisors greater than 1 with the preceding Fibonacci numbers, due to the identity: [6]
Graph of number of coupons, n vs the expected number of trials (i.e., time) needed to collect them all E (T ) In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests.