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A giraffe graph is a graph formed by all possible moves of a hypothetical chess piece called a "giraffe" which moves analogously to a knight except that it is restricted to ...

Any composite number n with p|(n/p-1) for all prime divisors p of n. n is a Giuga number iff sum_(k=1)^(n-1)k^(phi(n))=-1 (mod n) (1) where phi is the totient function and ...

If n>1 and n|1^(n-1)+2^(n-1)+...+(n-1)^(n-1)+1, is n necessarily a prime? In other words, defining s_n=sum_(k=1)^(n-1)k^(n-1), does there exist a composite n such that s_n=-1 ...

The continued fraction of A is [1; 3, 1, 1, 5, 1, 1, 1, 3, 12, 4, 1, 271, 1, ...] (OEIS A087501). A plot of the first 256 terms of the continued fraction represented as a ...

Let there be m doctors and n<=m patients, and let all mn possible combinations of examinations of patients by doctors take place. Then what is the minimum number of surgical ...

The Goddard-Henning graph, illustrated above in several embeddings, is the 9-node planar graph of graph diameter 2 having domination number gamma=3. It was first constructed ...

Consider the recurrence relation x_n=(1+x_0^2+x_1^2+...+x_(n-1)^2)/n, (1) with x_0=1. The first few iterates of x_n are 1, 2, 3, 5, 10, 28, 154, ... (OEIS A003504). The terms ...

A number of strongly regular graphs of several types derived from combinatorial design were identified by Goethals and Seidel (1970). Theorem 2.4 of Goethals and Seidel ...

The Golay code is a perfect linear error-correcting code. There are two essentially distinct versions of the Golay code: a binary version and a ternary version. The binary ...

The golden triangle, sometimes also called the sublime triangle, is an isosceles triangle such that the ratio of the hypotenuse a to base b is equal to the golden ratio, ...