On integer solutions to x² - dy² = 1, z² - 2dy² =1
On integers generated by a finite number of fixed primes
On integers n with for .
On integers nonrepresentable by a generalized arithmetic progression.
On integers not of the form n - φ (n)
W. Sierpiński asked in 1959 (see [4], pp. 200-201, cf. [2]) whether there exist infinitely many positive integers not of the form n - φ(n), where φ is the Euler function. We answer this question in the affirmative by proving Theorem. None of the numbers (k = 1, 2,...) is of the form n - φ(n).
On integers of the form
On integers with a special divisibility property
In this note, we study those positive integers which are divisible by , where is the Carmichael function.
On integers with many small prime factors
On integer-sequence-based constructions of generalized Pascal triangles.
On integral normal bases over intermediary fields
On integral representations by totally positive ternary quadratic forms
Let be a totally real algebraic number field whose ring of integers is a principal ideal domain. Let be a totally definite ternary quadratic form with coefficients in . We shall study representations of totally positive elements by . We prove a quantitative formula relating the number of representations of by different classes in the genus of to the class number of , where is a constant depending only on . We give an algebraic proof of a classical result of H. Maass on representations...
On integral similitude matrices
We study integral similitude 3 × 3-matrices and those positive integers which occur as products of their row elements, when matrices are symmetric with the same numbers in each row. It turns out that integers for which nontrivial matrices of this type exist define elliptic curves of nonzero rank and are closely related to generalized cubic Fermat equations.
On integral Stark conjectures (and multiplicative Galois module structures).
On integral Witt equivalence of algebraic number fields
On Integrality of Certain Algebraic Numbers Associated with Modular Forms.
On Integrality of Eisenstein Liftings.
On interaction of Hecke-Shimura rings: symplectic versus orthogonal
On interpolation functions of the generalized twisted -Euler polynomials.
On intervals containing full sets of conjugates of algebraic integers
On Invariant Measures, Minimal Sets and a Lemma of Margulies.