On products of singular elements
On R. Chapman's "evil determinant": case p ≡ 1 (mod 4)
For p ≡ 1 (mod 4), we prove the formula (conjectured by R. Chapman) for the determinant of the (p+1)/2 × (p+1)/2 matrix with .
On rational and integral roots of a polynomial
On real polynomials without nonnegative roots.
On sequences of numbers and polynomials defined by linear recurrence relations of order 2.
On S-Equivalence of Seifert Matrices.
On some polynomials allegedly related to the abc conjecture
On sums of four cubes of polynomials
On ternary inclusion-exclusion polynomials.
On the central coefficients of Bell matrices.
On the coefficients of the cyclotomic polynomial
On the divisibility of polynomials with integer coefficients.
On the divisibility of power LCM matrices by power GCD matrices
Let be a set of distinct positive integers and an integer. Denote the power GCD (resp. power LCM) matrix on having the -th power of the greatest common divisor (resp. the -th power of the least common multiple ) as the -entry of the matrix by (resp. . We call the set an odd gcd closed (resp. odd lcm closed) set if every element in is an odd number and (resp. ) for all . In studying the divisibility of the power LCM and power GCD matrices, Hong conjectured in 2004 that...
On the Fibonacci -matrices of order .
On the generalization of the Fibonacci-coefficient polynomials.
On the height of cyclotomic polynomials
On the irreducibility of 0,1-polynomials of the form f(x)xⁿ + g(x)
If f(x) and g(x) are relatively prime polynomials in ℤ[x] satisfying certain conditions arising from a theorem of Capelli and if n is an integer > N for some sufficiently large N, then the non-reciprocal part of f(x)xⁿ + g(x) is either identically ±1 or is irreducible over the rationals. This result follows from work of Schinzel in 1965. We show here that under the conditions that f(x) and g(x) are relatively prime 0,1-polynomials (so each coefficient is either 0 or 1) and f(0) = g(0) = 1, one...
On the irreducibility of -quadrinomials.
On the Irreducibility of Polynomials Taking Small Values.
On the irreducibility of some polynomials in two variables