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The upper half-plane is the portion of the complex plane {x+iy:x,y in (-infty,infty)} satisfying y=I[z]>0 i.e., {x+iy:x in (-infty,infty),y in (0,infty)}. Common notations ...

The divisor function sigma_k(n) for n an integer is defined as the sum of the kth powers of the (positive integer) divisors of n, sigma_k(n)=sum_(d|n)d^k. (1) It is ...

A Mersenne prime is a Mersenne number, i.e., a number of the form M_n=2^n-1, that is prime. In order for M_n to be prime, n must itself be prime. This is true since for ...

In general, an integer n is divisible by d iff the digit sum s_(d+1)(n) is divisible by d. Write a positive decimal integer a out digit by digit in the form ...

The term limit comes about relative to a number of topics from several different branches of mathematics. A sequence x_1,x_2,... of elements in a topological space X is said ...

The probability P(a,n) that n random arcs of angular size a cover the circumference of a circle completely (for a circle with unit circumference) is ...

Computational number theory is the branch of number theory concerned with finding and implementing efficient computer algorithms for solving various problems in number ...

Let P, Q be integers satisfying D=P^2-4Q>0. (1) Then roots of x^2-Px+Q=0 (2) are a = 1/2(P+sqrt(D)) (3) b = 1/2(P-sqrt(D)), (4) so a+b = P (5) ab = 1/4(P^2-D) (6) = Q (7) a-b ...

There are several regular mathematics competitions available to students. The International Mathematical Olympiad is perhaps the largest, while the William Lowell Putnam ...

A number is said to be pandigital if it contains each of the digits from 0 to 9 (and whose leading digit must be nonzero). However, "zeroless" pandigital quantities contain ...