593 research outputs found
Primitive divisors of Lucas and Lehmer sequences
Stewart reduced the problem of determining all Lucas and Lehmer sequences
whose -th element does not have a primitive divisor to solving certain Thue
equations. Using the method of Tzanakis and de Weger for solving Thue
equations, we determine such sequences for . Further computations
lead us to conjecture that, for , the -th element of such sequences
always has a primitive divisor
On the Diophantine equation
In this paper we consider the Diophantine equation where
are integer unknowns with and are odd primes and
We prove that there are only finitely many solutions
for which is not a sum of two consecutive squares. We also
study the above equation with fixed and with fixed $q.
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