Search Results for ""

Let omega be the cube root of unity (-1+isqrt(3))/2. Then the Eisenstein primes are Eisenstein integers, i.e., numbers of the form a+bomega for a and b integers, such that ...

The number 1000000=10^6. While one million in the "American" system of numbers means the same thing as one million in the "British" system, the words billion, trillion, etc., ...

Let p be an odd prime and F_n the cyclotomic field of p^(n+1)th roots of unity over the rational field. Now let p^(e(n)) be the power of p which divides the class number h_n ...

In general, a remainder is a quantity "left over" after performing a particular algorithm. The term is most commonly used to refer to the number left over when two integers ...

Let f(1)=1, and let f(n) be the number of occurrences of n in a nondecreasing sequence of integers. then the first few values of f(n) are 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, ... ...

A transformation x^'=Ax is unimodular if the determinant of the matrix A satisfies det(A)=+/-1. A necessary and sufficient condition that a linear transformation transform a ...

Yahtzee is a game played with five 6-sided dice. Players take turns rolling the dice, and trying to get certain types of rolls, each with an assigned point value, as ...

The complex plane is the plane of complex numbers spanned by the vectors 1 and i, where i is the imaginary number. Every complex number corresponds to a unique point in the ...

A Smarandache prime is a prime Smarandache number, i.e., a prime number of the form 1234...n. Surprisingly, no Smarandache primes are known as of Nov. 2015. Upper limits on ...

In the 1980s, Samuel Yates defined a titanic prime to be a prime number of at least 1000 decimal digits. The smallest titanic prime is 10^(999)+7. As of 1990, more than 1400 ...