文摘
Let class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301950&_mathId=si1.gif&_user=111111111&_pii=S0022314X16301950&_rdoc=1&_issn=0022314X&md5=80fd073b673319438f9f3cd71a6c610c" title="Click to view the MathML source">b(n)class="mathContainer hidden">class="mathCode"> denote the number of cubic partition pairs of n . This paper aims to study the congruences for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301950&_mathId=si1.gif&_user=111111111&_pii=S0022314X16301950&_rdoc=1&_issn=0022314X&md5=80fd073b673319438f9f3cd71a6c610c" title="Click to view the MathML source">b(n)class="mathContainer hidden">class="mathCode"> modulo 27. We first establish three Ramanujan type congruences. Then many infinite families of congruences are presented. Finally, we propose two conjectures on the congruences for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301950&_mathId=si1.gif&_user=111111111&_pii=S0022314X16301950&_rdoc=1&_issn=0022314X&md5=80fd073b673319438f9f3cd71a6c610c" title="Click to view the MathML source">b(n)class="mathContainer hidden">class="mathCode"> modulo class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301950&_mathId=si2.gif&_user=111111111&_pii=S0022314X16301950&_rdoc=1&_issn=0022314X&md5=cd47c3c14f14f38fcdbda6ff225b7325" title="Click to view the MathML source">49,81class="mathContainer hidden">class="mathCode"> and 243.