This paper is an attempt to apply the tools of supergeometry to arithmetic. Supergeometric objects are defined over supercommutative rings of coefficients. We consider an integral ring with two odd variables. In this case the even quantities, such as numbers and continued fractions, are dual integers, having both a classical and a nilpotent part. We refer to the nilpotent part as the “shadow”. We investigate the notions of supersymmetric continued fractions and the orthosymplectic modular group, and make some initial steps toward studying their properties.