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

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...

19, 91, 133, 247, and 1729. It is the third Carmichael number, and the first Chernick–Carmichael number. Furthermore, it is the first in the family of...

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

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...

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 palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16361) that remains the same when its digits are...

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...

The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes...

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

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...

other hand, the 33rd triangular number 561 is the first Carmichael number. 33 is also the first non-trivial dodecagonal number (like 369, and 561) and the...

recreational mathematics, a vampire number (or true vampire number) is a composite natural number with an even number of digits, that can be factored into...

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...

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...

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...

- 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...

In number theory, a semiperfect number or pseudoperfect number is a natural number n that is equal to the sum of all or some of its proper divisors. A...

10570 = weird number 10585 = Carmichael number 10601 = palindromic prime in bases 10 (1060110) and 30 (BNB30) 10609 = 1032, tribonacci number 10631 = palindromic...

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

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...

doi:10.2307/2031878, JSTOR 2031878 Yabuta, M. (2001), "A simple proof of Carmichael's theorem on primitive divisors" (PDF), Fibonacci Quarterly, 39 (5): 439–443...

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...

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

In number theory, a self number or Devlali number in a given number base b {\displaystyle b} is a natural number that cannot be written as the sum of...

In mathematics, a double Mersenne number is a Mersenne number of the form M M p = 2 2 p − 1 − 1 {\displaystyle M_{M_{p}}=2^{2^{p}-1}-1} where p is prime...

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...

Cullen number is a member of the integer sequence C n = n ⋅ 2 n + 1 {\displaystyle C_{n}=n\cdot 2^{n}+1} (where n {\displaystyle n} is a natural number). Cullen...

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...