In number theory, a Carmichael number is a composite number ⁠ n {\displaystyle n} ⁠ which in modular arithmetic satisfies the congruence relation: b n...

13\times 19} . Relatedly, it is the third Carmichael number, and specifically the first Chernick–Carmichael number. Furthermore, it is the first in the family...

In mathematics, a Lucas–Carmichael number is a positive composite integer n such that if p is a prime factor of n, then p + 1 is a factor of n + 1; n...

the number 1 differently than larger numbers, sometimes even not as a number at all. Euclid, for example, defined a unit first and then a number as a...

Carmichael may refer to: Carmichael (surname) Clan Carmichael, Scottish clan Carmichael, California, United States Carmichael coal mine, a proposed mine...

F6 and F12) every Fibonacci number has a prime factor that is not a factor of any smaller Fibonacci number (Carmichael's theorem). As a result, 8 and...

A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has...

A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that...

A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16461) that remains the same when its digits are...

In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the sieve of Eratosthenes...

triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples...

In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number...

In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with...

In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy...

they were previously discovered in the 1730s by Minggatu. The n-th Catalan number can be expressed directly in terms of the central binomial coefficients...

- 1 is prime 2015 – Lucas–Carmichael number 2016 – triangular number, number of 5-cubes in a 9-cube, Erdős–Nicolas number, 211-25 2017 – Mertens function...

mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer...

In mathematics, a polygonal number is a number that counts dots arranged in the shape of a regular polygon: 2-3 . These are one type of 2-dimensional figurate...

Friedman number 100,489 = 3172, the smallest 6-digit square 101,101 = smallest palindromic Carmichael number 101,723 = smallest prime number whose square...

In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The...

numbers two terms apart in the Fibonacci sequence results in the Lucas number in between. The first few Lucas numbers are 2, 1, 3, 4, 7, 11, 18, 29, 47...

In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so...

In number theory, an n-smooth (or n-friable) number is an integer whose prime factors are all less than or equal to n. For example, a 7-smooth number is...

number 5671 – triangular number 5701 – super-prime, prime of the form 2p-1 5711 – Sophie Germain prime 5719 – Zeisel number, Lucas–Carmichael number 5741...

the number of cubic inches in a cubic foot, palindromic in base 11 (133111) and 23 (36323) 1729 = taxicab number, Carmichael number, Zeisel number, centered...

number of regular simple graphs on 7 labeled nodes 933 = 3 × 311 934 = 2 × 467, nontotient 935 = 5 × 11 × 17, sphenic number, Lucas–Carmichael number...

are not primes), Carmichael's totient function conjecture, Carmichael's theorem, and the Carmichael function, all significant in number theory and in the...

A pronic number is a number that is the product of two consecutive integers, that is, a number of the form n ( n + 1 ) {\displaystyle n(n+1)} . The study...

A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron...

Markov number 51984 = 2282 = 373 + 113. the smallest square to the sum of only five distinct fourth powers. 52488 = 3-smooth number 52633 = Carmichael number...