Ars Combinatoria, vol.85, pp.257-269, 2007 (SCI-Expanded)
Let F(x, y) = ax2; + bxy + cy2 be a binary quadratic form of discriminant Δ = b2 - 4ac for a, b, c ∈ Z, let p be a prime number and let Fp be a finite field. In this paper we formulate the number of integer solutions of cubic congruence x3 + ax2 + bx + c ≡ 0 (mod p) over Fp for two specific binary quadratic forms Flk (x, y) = x2 + kxy + ky2 and F2k(x, y) = kxy + kxy + k 2y2 for integer k such that 1 < k < 9. Later we consider representation of primes by F1k and F 2k.