We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Let 
$Q(n)$ denote the number of partitions of n into distinct parts. Merca [‘Ramanujan-type congruences modulo 4 for partitions into distinct parts’, An. Şt. Univ. Ovidius Constanţa 30(3) (2022), 185–199] derived some congruences modulo 
$4$ and 
$8$ for 
$Q(n)$ and posed a conjecture on congruences modulo powers of 
$2$ enjoyed by 
$Q(n)$. We present an approach which can be used to prove a family of internal congruence relations modulo powers of 
$2$ concerning 
$Q(n)$. As an immediate consequence, we not only prove Merca’s conjecture, but also derive many internal congruences modulo powers of 
$2$ satisfied by 
$Q(n)$. Moreover, we establish an infinite family of congruence relations modulo 
$4$ for 
$Q(n)$.
