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Consider an n-digit number k. Square it and add the right n digits to the left n or n-1 digits. If the resultant sum is k, then k is called a Kaprekar number. For example, 9 ...

Given a hereditary representation of a number n in base b, let B[b](n) be the nonnegative integer which results if we syntactically replace each b by b+1 (i.e., B[b] is a ...

A plane partition is a two-dimensional array of integers n_(i,j) that are nonincreasing both from left to right and top to bottom and that add up to a given number n. In ...

Also called "Ethiopian multiplication." To multiply two numbers a and b, write a_0=a and b_0=b in two columns. Under a_0, write |_a_0/2_|, where |_x_| is the floor function, ...

A root of a polynomial P(z) is a number z_i such that P(z_i)=0. The fundamental theorem of algebra states that a polynomial P(z) of degree n has n roots, some of which may be ...

A magic hexagon of order n is an arrangement of close-packed hexagons containing the numbers 1, 2, ..., H_(n-1), where H_n is the nth hex number such that the numbers along ...

Write down the positive integers in row one, cross out every k_1th number, and write the partial sums of the remaining numbers in the row below. Now cross off every k_2th ...

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

The first few numbers not known to produce palindromes when applying the 196-algorithm (i.e., a reverse-then-add sequence) are sometimes known as Lychrel numbers. This term ...

A friend of a number n is another number m such that (m,n) is a friendly pair.