Abstract

Ramanujan was the first mathematician to discover some of the arithmetical properties of p(n), the number of unrestricted partitions of n. His congruence,for example, is famous [2; 3]. Some progress has been made since then; it is known that the congruence,has an infinitude of solutions for any arbitrary value of r [4]. This is a somewhat weak relation, and one would have liked to obtain, if possible, stronger results of the type,for ‘almost all’ values of n, which in its turn is derivable from another stronger relation, viz.,also established by Ramanujan [2], where r(n) is Ramanujan's function defined by

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