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In number theory, a self number or Devlali number in a given number base is a natural number that cannot be written as the sum of any other natural number and the individual digits of . 20 is a self number (in base 10), because no such combination can be found (all < give a result less than 20; all other give a result greater than 20). 21 is not, because it can be written as 15 + 1 + 5 using n ...
Another class of numbers Kaprekar described are Kaprekar numbers. [10] A Kaprekar number is a positive integer with the property that if it is squared, then its representation can be partitioned into two positive integer parts whose sum is equal to the original number (e.g. 45, since 45 2 =2025, and 20+25=45, also 9, 55, 99 etc.)
Since f is of degree d with integer coefficients, if a and b are integers, then so will be b d ·f(a/b), which we call r. Similarly, s = b e ·g(a/b) is an integer. The goal is to find integer values of a and b that simultaneously make r and s smooth relative to the chosen basis of primes.
The integers arranged on a number line. An integer is the number zero , a positive natural number (1, 2, 3, . . .), or the negation of a positive natural number (−1, −2, −3, . . .). [1] The negations or additive inverses of the positive natural numbers are referred to as negative integers. [2]
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."
Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function fields.
In mathematics, a self-descriptive number is an integer m in a given base b that is b digits long, and each digit d at position n (the most significant digit being at position 0 and the least significant at position b−1) counts how many instances of digit n are in m.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.