Triples of Positive Integers with the same Sum and the same Product
It is proved that for every k there exist k triples of positive integers with the same sum and the same product.
Trivial points on towers of curves
In order to study the behavior of the points in a tower of curves, we introduce and study trivial points on towers of curves, and we discuss their finiteness over number fields. We relate the problem of proving that the only rational points are the trivial ones at some level of the tower, to the unboundeness of the gonality of the curves in the tower, which we show under some hypothesis.
Truncated Units in Infinitely many Algebraic Number Fields of Degree n...4.
Two Diophantine approaches to the irreducibility of certain trinomials
Two Diophantine Systems.
Two divisors of summing up to
In this short note, we give an affirmative answer to a question of Ayad from [1].
Two equations for linear recurrence sequences
Two exponential diophantine equations
The equation , to be solved in non-negative rational integers , has been mentioned by Masser as an example for which there is still no algorithm to solve completely. Despite this, we find here all the solutions. The equation , to be solved in non-negative rational integers and a rational integer , has been mentioned by Corvaja and Zannier as an example for which the number of solutions is not yet known even to be finite. But we find here all the solutions too; there are in fact only six.
Two remarks on linear forms in non-negative integers.