Inspired by the work of Ramanujan on the standard partition function p(n), Chan [4] asked whether there are any other

congruence properties of the following form: [c.

Key words: Modular Arithmetic,

Congruence, Divisibility, b-adic expension.

It is the smallest

congruence containing both ~ and [approximately equal to];

Some single-country longitudinal studies have tried to explain opinion-policy

congruence using variables that do vary in the medium run, like the party in power or the size of the majority in parliament.

Waldherr, On certain explicit

congruences for mock theta functions, Proc.

Since we are interested in first order

Congruences, we may need that the

congruence B splits in some components.

Thus it becomes interesting to find solutions of

congruences of the type Equation through Numerical Analysis as this is the generalization of the above case in a sense that if Equation is substituted in last equation then all of the results for finding the inverse of numbers modulo prime powers are produced.

q-analogs of the binomial coefficient

congruences of Babbage, Wolstenholme and Glaisher.

Let C(S) be the set of all

congruences on S and let A[sigma] be the set {a [member of] S| ([there exists]x [member of] A) (a, x) [member of] [sigma]} for any [sigma] [member of] C(S).

There's nothing about the definition of partitions that gives an easy explanation for why the three Ramanujan

congruences exist" These

congruences forge a link between two ways of expressing numbers--as sums and as products.

The motivation for the definition of shards arises from the study of lattice

congruences of the weak order, and will be discussed in Section 5.

Nothing in the definition of partitions hinted that such relationships, called

congruences, should exist or that the prime numbers 5, 7, and 11 should play a special role.