Number theory

ambiguous mathematical term used either for non-negative or for strictly positive integers, depending on usage

branch of pure mathematics devoted primarily to the study of the integers

smallest positive integer divisible by two or more integers

two numbers whose only common factor is 1

product of some integer with itself

function which gives the number of integers relatively prime to and not greater than its input

rational number sequence 𝐵ₖ such that (𝑚+1)∑𝑛ᵐ=(ᵐ⁺¹₀)𝐵₀𝑛ᵐ⁺¹−(ᵐ⁺¹₁)𝐵₁𝑛ᵐ+(ᵐ⁺¹₂)𝐵₂𝑛ᵐ¯¹−(ᵐ⁺¹₃)𝐵₃𝑛ᵐ¯²+⋯

major branch of number theory

In mathematics, the remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient (integer division). In algebra of polynomials, the remainder is the polynomial "left over" after dividing one polynomial by another. The modulo operation is the operation that produces such a remainder when given a dividend and divisor.

mathematical problem

product of a number being raised to the third power

arithmetic function that is multiplicative for every pair of coprime integers

integer that cannot be divided by a square number

number system for a prime p which extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems

number theory conjecture

number

non-negative integer, the representation of whose square in that base can be split into two parts that add up to the original number again

numbers whose aliquot sums form a cyclic sequence

finite sum of distinct unit fractions

book written by Carl Friedrich Gauss

smallest number that can be expressed as a sum of two positive cube numbers in n distinct ways

conjecture

real number whose infinite sequence of digits in every positive integer base is distributed uniformly

arithmetic function related to the divisors of an integer

positive integer that is an integer power of another positive integer

number equal to a partial sum of the harmonic series: the sum of the first n whole number reciprocals; 1/1 + 1/2 + 1/3 + ... + 1/n

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integer whose multiples are digit permutations

polynomial sequence

positive integer power of a prime number

one of two prizes awarded by the American Mathematical Society

result of multiplying four instances of a natural number together

increasing sequence of reduced fractions between 0 and 1 whose denominators do not exceed a given positive integer

decimal number formed by concatenating successive representations of integers

sum of a number's digits

irreducible polynomial of integer coefficients whose roots are nth roots of unity

study of algorithms for performing number theoretic computations

set of marks at integer positions along an imaginary ruler such that no two pairs of marks are the same distance apart

award

integer sequence in which each member of the sequence is the product of the previous members, plus one

mathematical method to measure sets of natural numbers

a natural number whose square "ends" in the same digits as the number itself

repeated digital sum

rational number whose denominator is a power of two

q-analog of the Pochhammer symbol

math function by Srinivasa Ramanujan

the sum of the first n cubes, which equals the square of the nth triangular number

positive integer whose divisors have a harmonic mean that is an integer

result of multiplying five instances of a natural number together

the mathematical function ∏ₖ₌₁^∞ (1−𝑞ᵏ)

formula used in number theory to compute series

complex numbers with positive imaginary part

mathematical constant

irrational root of a quadratic equation with integer coefficients

branch of number theory that deals with the analysis of functions of p-adic numbera

result of multiplying six instances of a number

node-link graph of elements of a finite field, adjacent when their difference is a quadratic residue

mathematical function related to the gamma function