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A magic square is a square array of numbers consisting of the distinct positive integers 1, 2, ..., n^2 arranged such that the sum of the n numbers in any horizontal, ...

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 Kaprekar routine is an algorithm discovered in 1949 by D. R. Kaprekar for 4-digit numbers, but which can be generalized to k-digit numbers. To apply the Kaprekar routine ...

The Tilley graph is a polyhedral graph that arises in the investigation of Kempe chainsKempe Chain (Tilley 2018). It has 12 vertices, 29 edges, and 19 faces (one of which is ...

The Smarandache function mu(n) is the function first considered by Lucas (1883), Neuberg (1887), and Kempner (1918) and subsequently rediscovered by Smarandache (1980) that ...

A circulant graph is a graph of n graph vertices in which the ith graph vertex is adjacent to the (i+j)th and (i-j)th graph vertices for each j in a list l. The circulant ...

Kontsevich's integral is a far-reaching generalization of the Gauss integral for the linking number, and provides a tool to construct the universal Vassiliev invariant of a ...

Triskaidekaphobia is the fear of 13, a number commonly associated with bad luck in Western culture. While fear of the number 13 can be traced back to medieval times, the word ...

A theory is decidable iff there is an algorithm which can determine whether or not any sentence r is a member of the theory.

There are at least two results known as "the area principle." The geometric area principle states that (|A_1P|)/(|A_2P|)=(|A_1BC|)/(|A_2BC|). (1) This can also be written in ...