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Stanley's theorem states that the total number of 1s that occur among all unordered partitions of a positive integer is equal to the sum of the numbers of distinct members of ...

where _5F_4(a,b,c,d,e;f,g,h,i;z) is a generalized hypergeometric function and Gamma(z) is the gamma function. Bailey (1935, pp. 25-26) called the Dougall-Ramanujan identity ...

Let X_1,X_2 subset P^2 be cubic plane curves meeting in nine points p_1, ..., p_9. If X subset P^2 is any cubic containing p_1, ..., p_8, then X contains p_9 as well. It is ...

For all integers n and |x|<a, lambda_n^((t))(x+a)=sum_(k=0)^infty|_n; k]lambda_(n-k)^((t))(a)x^k, where lambda_n^((t)) is the harmonic logarithm and |_n; k] is a Roman ...

Taylor's theorem states that any function satisfying certain conditions may be represented by a Taylor series, Taylor's theorem (without the remainder term) was devised by ...

The fundamental theorem of arithmetic states that every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of ...

Let the opposite sides of a convex cyclic hexagon be a, a^', b, b^', c, and c^', and let the polygon diagonals e, f, and g be so chosen that a, a^', and e have no common ...

A theorem in game theory which guarantees the existence of a set of mixed strategies for finite, noncooperative games of two or more players in which no player can improve ...

Markov's theorem states that equivalent braids expressing the same link are mutually related by successive applications of two types of Markov moves. Markov's theorem is ...

A generalization of Fermat's little theorem. Euler published a proof of the following more general theorem in 1736. Let phi(n) denote the totient function. Then a^(phi(n))=1 ...