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If there is a (nu,nu^') correspondence between two curves of curve genus p and p^' and the number of branch points properly counted are beta and beta^', then ...

If three circles A, B, and C are taken in pairs, the external similarity points of the three pairs lie on a straight line. Similarly, the external similarity point of one ...

Let three equal circles with centers J_A, J_B, and J_C intersect in a single point H and intersect pairwise in the points A, B, and C. Then the circumcircle O of the ...

Given any triangle ABC, the signed sum of perpendicular distances from the circumcenter O to the sides (i.e., signed lengths of the pedal lines from O) is OO_A+OO_B+OO_C=R+r, ...

Every "large" even number may be written as 2n=p+m where p is a prime and m in P union P_2 is the set of primes P and semiprimes P_2.

Let H be a heptagon with seven vertices given in cyclic order inscribed in a conic. Then the Pascal lines of the seven hexagons obtained by omitting each vertex of H in turn ...

There are at least two Siegel's theorems. The first states that an elliptic curve can have only a finite number of points with integer coordinates. The second states that if ...

Let G(V,E) be a graph with graph vertices V and graph edges E on n graph vertices without a (k+1)-clique. Then t(n,k)<=((k-1)n^2)/(2k), where t(n,k) is the edge count. (Note ...

Let G be a graph and S a subgraph of G. Let the number of odd components in G-S be denoted S^', and |S| the number of graph vertices of S. The condition |S|>=S^' for every ...

where _3F_2(a,b,c;d,e;z) is a generalized hypergeometric function and Gamma(z) is the gamma function (Bailey 1935, p. 16; Koepf 1998, p. 32).