Modular Arithmetic, Differences and Similarities . Modular Arithmetic Differences and Similarities Modular arithmetic is very similar to the Arithmetic we are so much used to. 2 and 3 are zero divisors in the arithmetic modulo 6.
Euclidean arithmetic has no zero divisors.
Arithmetic modulo a prime, too, has no zero divisors. Polynomial roots Fundamental Theorem of Algebra implies that every polynomial of order n over the field C of complex numbers has exactly n roots. In the Gaussian arithmetic all depends on a polynomial. In arithmetic modulo a prime number p, every non-zero number has an inverse. But of course there is a good deal of similarity between the two arithmetic.