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The number of digits D in an integer n is the number of numbers in some base (usually 10) required to represent it. The numbers 1 to 9 are therefore single digits, while the ...

A general quadratic Diophantine equation in two variables x and y is given by ax^2+cy^2=k, (1) where a, c, and k are specified (positive or negative) integers and x and y are ...

The Euclidean algorithm, also called Euclid's algorithm, is an algorithm for finding the greatest common divisor of two numbers a and b. The algorithm can also be defined for ...

A graceful graph is a graph that can be gracefully labeled. Special cases of graceful graphs include the utility graph K_(2,3) (Gardner 1983) and Petersen graph. A graph that ...

A Hadamard matrix is a type of square (-1,1)-matrix invented by Sylvester (1867) under the name of anallagmatic pavement, 26 years before Hadamard (1893) considered them. In ...

In this work, the name Pythagoras's constant will be given to the square root of 2, sqrt(2)=1.4142135623... (1) (OEIS A002193), which the Pythagoreans proved to be ...

In his Meditationes algebraicae, Waring (1770, 1782) proposed a generalization of Lagrange's four-square theorem, stating that every rational integer is the sum of a fixed ...

The 11-cell is a regular 4-dimensional structure that cannot be represented in 3-dimensional space in any reasonable way and is highly self-intersecting even in 4-dimensional ...

Calculating the 13th root of a large number (that is a perfect 13th power) is a famous mental calculation challenge. However, because of difficulties in standardizing the ...

A 30-60-90 triangle is a right triangle having angles of 30 degrees, 60 degrees, and 90 degrees. For a 30-60-90 triangle with hypotenuse of length a, the legs have lengths b ...