International Journal of Science and Technology (IJST)

Further congruences for [j,k]- overpartition with even parts distinct

: Naika, MS Mahadeva, Harishkumar T, and T. N. Veeranayaka[4] defined (ped) ̅_(j,k) (n) as the number of [j, k]- overpartitions of a positive integer n with the restriction that even parts are distinct and the first occurrence of each distinct part congruent to j modulo k may be overlined. In this paper some infinite families of congruence modulo power of 2 of (ped) ̅_(3,3) (n) and (ped) ̅_(3,6) (n) will be established, such as (ped) ̅_(3,3) (6.p^(2α+1).(pn+w)+(13.p^(2α+2)-1)/4)=0 (mod 8) (ped) ̅_(3,6) (24.p^(2α+1).(pn`+m)+13.p^(2α+2) ) q^(n )≡0 (mod 4)