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The Randić index of a graph is defined as half the sum of the matrix elements of its Randić matrix. While the index was introduced to model the branching of the carbon-atom ...

The Randić spectral radius rho_(Randic) of a graph is defined as the largest eigenvalue of its Randić matrix.

Let the minimal length of an addition chain for a number n be denoted l(n). Then the Scholz conjecture, also called the Scholz-Brauer conjecture or Brauer-Scholz conjecture, ...

For any M, there exists a t^' such that the sequence n^2+t^', where n=1, 2, ... contains at least M primes.

Let the divisor function d(n) be the number of divisors of n (including n itself). For a prime p, d(p)=2. In general, sum_(k=1)^nd(k)=nlnn+(2gamma-1)n+O(n^theta), where gamma ...

A 2-variable oriented knot polynomial P_L(a,z) motivated by the Jones polynomial (Freyd et al. 1985). Its name is an acronym for the last names of its co-discoverers: Hoste, ...

The Jacobian conjecture in the plane, first stated by Keller (1939), states that given a ring map F of C[x,y] (the polynomial ring in two variables over the complex numbers ...

Let A be the area of a simply closed lattice polygon. Let B denote the number of lattice points on the polygon edges and I the number of points in the interior of the ...

Find two distinct sets of integers {a_1,...,a_n} and {b_1,...,b_n}, such that for k=1, ..., m, sum_(i=1)^na_i^k=sum_(i=1)^nb_i^k. (1) The Prouhet-Tarry-Escott problem is ...

For a given m, determine a complete list of fundamental binary quadratic form discriminants -d such that the class number is given by h(-d)=m. Heegner (1952) gave a solution ...