engleski

Upper bound on number of D(4)-quintuples

We call the set of m positive distinct integers D(n)-m-tuple if the product of any of its two elements increased by n is a perfect square. It is conjectured that there does not exist a D(4)-quintuple and we will present some results that support that conjecture. We will show how we improved previous results on the upper bound of D(4)-quintuples, more precisely, we prove there is at most 6.8587⋅10^29 D(4)-quintuples. In the proof we use the standard methods used in solving similar problems, solving the system of simultaneous Pellian equations, and combine them with the most recent methods used for bounding the number of D(1)-quintuples.

Diophantine m-tuples

nije evidentirano