A note on pseudoprimes with respect to abelian linear recurring sequence. (English) Zbl 0888.11006

It is proved that, for any finite system of simple abelian linear recurring sequences \(\{a_n^i\}\), \(i\in I\), and arbitrary integer \(l\geq 3\), Schinzel’s conjecture H implies the existence of infinitely many composite numbers \(n\) which are a product of \(l\) different primes and satisfy \(a_{ns}^i \equiv a_s^i \pmod n\) for every natural number \(s\).


11A51 Factorization; primality
11B37 Recurrences
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