Generalizations of Problems of Pomerance on Residue Systems

<strong>Mathematics Seminar of the School of Physical Sciences ---------------------------------------------------------</strong> Title:&nbsp;<strong>Generalizations of Problems of Pomerance on Residue Systems</strong> Speaker:&nbsp;<strong>N. Saradha</strong>&nbsp; (Tata Institute of Fundamental Research, Mumbai) Date:&nbsp;<strong>September 8, 2016</strong> <strong>Abstract:</strong>&nbsp;In 1980, Pomerance showed that there are only finitely many integers k such that the first \varphi( k) primes coprime to k form a reduced residue system. He conjectured that any such k should be in {2,4,6,12,18,30}. This was solved by Yang and Togbe in 2014. We shall discuss the method involved and also some generalizations of this problem which are connected with Prime l-tuple conjecture.