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Let Delta denote an integral convex polytope of dimension n in a lattice M, and let l_Delta(k) denote the number of lattice points in Delta dilated by a factor of the integer ...

A Fermat prime is a Fermat number F_n=2^(2^n)+1 that is prime. Fermat primes are therefore near-square primes. Fermat conjectured in 1650 that every Fermat number is prime ...

A Gaussian sum is a sum of the form S(p,q)=sum_(r=0)^(q-1)e^(-piir^2p/q), (1) where p and q are relatively prime integers. The symbol phi is sometimes used instead of S. ...

In his monumental treatise Disquisitiones Arithmeticae, Gauss conjectured that the class number h(-d) of an imaginary quadratic field with binary quadratic form discriminant ...

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 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, ...

Let X be a set of urelements that contains the set N of natural numbers, and let V(X) be a superstructure whose individuals are in X. Let V(^*X) be an enlargement of V(X), ...

The problem of determining how many nonattacking knights K(n) can be placed on an n×n chessboard. For n=8, the solution is 32 (illustrated above). In general, the solutions ...

A short theorem used in proving a larger theorem. Related concepts are the axiom, porism, postulate, principle, and theorem. The late mathematician P. Erdős has often been ...

The five Mathieu groups M_(11), M_(12), M_(22), M_(23), and M_(24) were the first sporadic groups discovered, having been found in 1861 and 1873 by Mathieu. Frobenius showed ...