On perfect powers in products with terms from arithmetic progressions
On Pillai's Diophantine equation.
On polynomial-exponential equations.
On solutions of the equation Xⁿ + Yⁿ = BZⁿ with prime n|BZ
On some arithmetic properties of polynomial expressions involving Stirling numbers of the second kind
On some arithmetical properties of Lucas and Lehmer numbers
On some arithmetical properties of weighted sums of S-units.
On some generalizations of the diophantine equation
On some generalizations of the diophantine equation
On sums of -units and linear recurrences
On Terai's conjecture concerning Pythagorean numbers
On the abc conjecture in algebraic number fields
On the Brocard-Ramanujan problem and generalizations
Let denote the ith prime. We conjecture that there are precisely 28 solutions to the equation in positive integers n and α₁,..., . This conjecture implies an explicit description of the set of solutions to the Brocard-Ramanujan equation. We also propose another variant of the Brocard-Ramanujan problem: describe the set of solutions in non-negative integers of the equation n! + A = x₁²+x₂²+x₃² (A fixed).
On the difference between perfect powers
On the Diophantine equation 1 + x + y = z, with xyz = 2r3s7t.
On the Diophantine equation
Let be an odd prime. By using the elementary methods we prove that: (1) if , the Diophantine equation has no positive integer solution except when or is of the form , where is an odd positive integer. (2) if , , then the Diophantine equation has no positive integer solution.
On the diophantine equation
On the diophantine equation
On the Diophantine equation .
On the diophantine equation D₁x⁴ -D₂y² = 1