Mihai Prunescu

Short arithmetic terms for the cardinality of elliptic curves over rings of remainder classes and over finite fields

Arithmetic terms are fixed finite compositions of addition, truncated subtraction, multiplication, integer division and exponentiation on natural numbers. We construct such terms for the number of affine solutions of $ y^2 = x^3 + Ax + B $. For arbitrary moduli $ n \geq 1 $, a specialization of Prunescu's general const...