A curious identity of Bunyakovsky (1882), which was made more widely known by P ́olya and Szeg ̋o in their “Problems and Theorems in Analysis”, gives an evaluation of a sum of the floor function of square roots involving primes p ≡ 1 (mod 4). We evaluate this sum also in the case p ≡ 3 (mod 4), obtaining an identity in terms of the class number of the imaginary quadratic field Q(√−p). We also consider certain cases where the prime p is replaced by a composite integer. Class numbers of imaginary quadratic fields are again involved in some cases.

(Joint work with Marc Chamberland.)