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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.
First, it can be false in practice. A theoretical polynomial algorithm may have extremely large constant factors or exponents, rendering it impractical. For example, the problem of deciding whether a graph G contains H as a minor, where H is fixed, can be solved in a running time of O(n 2), [25] where n is the number of vertices in G.
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.
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.
The Armstrong Siddeley Python was an early British turboprop engine designed and built by the Armstrong Siddeley company in the mid-1940s. Its main use was in the Westland Wyvern, a carrier-based heavy fighter. The prototypes had used the Rolls-Royce Eagle piston engine, but Pythons were used in production aircraft.
Certain number-theoretic methods exist for testing whether a number is prime, such as the Lucas test and Proth's test. These tests typically require factorization of n + 1, n − 1, or a similar quantity, which means that they are not useful for general-purpose primality testing, but they are often quite powerful when the tested number n is ...
First, place the natural numbers along the top row. To determine a number in the table, take the number immediately to the left. Then use that number to look up the required number in the column given by that number and one row up. If there is no number to its left, simply look at the column headed "1" in the previous row.