Note on Egyptian fractions.
Note on Irregularities of Distibution.
Note on J. H. E. Cohn's paper "The Diophantine equation xⁿ = Dy² + 1"
Note on Lattice-Point-Free Convex Bodies.
Note on Legendre numbers.
Note on multiplicative functions satisfying congruence property. II.
Note on perfect and multiply perfect numbers
Note on primes of type x2 + 32y2, class number, and residuacity.
Note on -extensions of Euler numbers and polynomials of higher order.
Note on -Nasybullin's lemma associated with the modified -adic -Euler measure.
Note on sequences well-spaced and well-distributed among congruence classes
Note on some greatest common divisor matrices
Some quadratic forms related to "greatest common divisor matrices" are represented in terms of L²-norms of rather simple functions. Our formula is especially useful when the size of the matrix grows, and we will study the asymptotic behaviour of the smallest and largest eigenvalues. Indeed, a sharp bound in terms of the zeta function is obtained. Our leading example is a hybrid between Hilbert's matrix and Smith's matrix.
Note on some results of A.F. Horadam and A.G. Shannon concerning a Catalan's identity on Fibonacci numbers
Note on the Chebyshev polynomials and applications to the Fibonacci numbers.
Note on the class-number of the maximal real subfield of a cyclomatic field.
Note on the class-number of the maximal real subfield of a cyclomatic field.
Note on the congruence of Ankeny-Artin-Chowla type modulo p²
The results of [2] on the congruence of Ankeny-Artin-Chowla type modulo p² for real subfields of of a prime degree l is simplified. This is done on the basis of a congruence for the Gauss period (Theorem 1). The results are applied for the quadratic field ℚ(√p), p ≡ 5 (mod 8) (Corollary 1).
Note on the congruences , ,
Note on the cubic residues
Note on the degree of concavity of the determinant on sets of positive definite quadratic forms.