Diophantine m-tuples with elements in arithmetic progressions

作者：Dujella A^*; Saradha N

来源：Indagationes Mathematicae, 2014, 25(1): 131-136.

DOI：10.1016/j.indag.2013.08.006

• Diophantine m-tuples
• Arithmetic progressions
• Pellian equations

In this paper, we consider the problem of existence of Diophantine m-tuples which are (not necessarily consecutive) elements of an arithmetic progression. We show that for n %26gt;= 3 there does not exist a Diophantine quintuple {a, b, c, d, e} such that a equivalent to b equivalent to c equivalent to d equivalent to e(mod n). On the other hand, for any positive integer n there exist infinitely many Diophantine triples {a, b, c} such that a equivalent to b equivalent to c equivalent to 0(mod n).

• 出版日期2014-1-5