Abstract
Complex numbers whose real and imaginary parts are integers are called Gaussian integers. In this article, the well-known arithmetic functions—the number, sum and product of divisors—are generalized to Gaussian integers. For this functions, the formulae for calculation that use the prime factorization were derived, and some properties of these functions that concern associative or conjugate Gaussian integers were established. Obtained were also the formulae of the number, sum and product of all divisors of a Gaussian integer that are themselves divisible by a certain number. The usefulness of the obtained results are illustrated in the solutions to some problems.
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