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The logarithm log_bx for a base b and a number x is defined to be the inverse function of taking b to the power x, i.e., b^x. Therefore, for any x and b, x=log_b(b^x), (1) or ...

Sudoku (literally, "single number"), sometimes also is a pencil-and-paper logic puzzle whose goal is to complete a grid satisfying various constraints. In the "classic" ...

An algorithm for making tables of primes. Sequentially write down the integers from 2 to the highest number n you wish to include in the table. Cross out all numbers >2 which ...

An (n,k)-talisman hexagon is an arrangement of nested hexagons containing the integers 1, 2, ..., H_n=3n(n-1)+1, where H_n is the nth hex number, such that the difference ...

Let sigma_0(n) and sigma_1(n) denote the number and sum of the divisors of n, respectively (i.e., the zeroth- and first-order divisor functions). A number n is called sublime ...

If a prime number divides a norm but not the bases of the norm, it is itself a norm.

A number v=xy with an even number n of digits formed by multiplying a pair of n/2-digit numbers (where the digits are taken from the original number in any order) x and y ...

A number which can be specified implicitly or explicitly by exponential, logarithmic, and algebraic operations.

F_mF_(n+1)-F_nF_(m+1)=(-1)^nF_(m-n), where F_n is a Fibonacci number.

A number of the form p^a·A is said to be an antisquare if it fails to be a square number for the two reasons that a is odd and A is a nonsquare (modulo p). The first few ...