Abstract

In 2008, Lovejoy and Osburn defined the generating function for Pn .In 2009, Byungchan Kim defined the generating function for P n 2 .This paper shows how to discuss the generating functions for Pn and P n 2 . Byungchan Kim also defined P n k with increasing relation and overpartition congruences mod 4,8 and 64. In 2006, Berndt found the relation ( ) ( ) d1,4 n  d3,4 n has two values with certain restrictions and various formulae by the common term (n) .This paper shows how to prove the four Theorems about overpartitions modulo 8.These Theorems satisfy the arithmetic properties of the overpartition function modulo 8.

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