Abstract: In Number theory , Ramanujan's sum, usually denoted cq(n), is a function of two positive integer variables q and n defined by the formula. where (a, q) = 1 means that a only takes on values coprime to q. Also a real or complex valued function defined on the set of all positive integers is called an arithmetic function and an arithmetic function is said to be completely multiplicative function if f is not identically zero and f(mn) = f(m)f(n) for all m,n. we know the reduced residue system modulo N is the set of all integers m with gcd (m,N) = 1 and 0 ≤ m ≤ N.......
Key Word: Ramanujan sum, Arithmetic function, Multiplicative function, reduced residue system modulo integer
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