The number of equations c=a+b satisfying the abc-conjecture
The number of extensions of a number field with fixed degree and bounded discriminant
The number of Goldbach representations of an integer
The number of Hecke eigenvalues of same signs
The number of imaginary quadratic fields with a given class number
The number of integer points in a family of anisotropically expanding domains
The number of iterates of the Carmichael lambda function required to reach 1
The number of nonzero binomial coefficients modulo p^alpha
The number of points on an elliptic curve with square x-coordinates
The number of rational numbers determined by large sets of integers
The number of self-conjugate core partitions
The number of solutions of an equation related to a product of multilinear polynomials
The number of solutions of lambda(x)=n
The odd Catalan numbers modulo 2^k
The Ongoing Binomial Revolution
The Optimal Isodual Lattice Quantizer in Three Dimensions
The optimality of the Boundedness Height Conjecture
The Ostrogradsky series and related probability measures
The Other Group of as Galois Extension
The overconvergent Shimura lifting