  This paper is an attempt to apply the tools of supergeometry to arithmetic.
Supergeometric objects are defined over supercommutative rings of coefficients,
and we consider an integral ring with exactly two odd variables. In this case
the even quantities, such as numbers and continued fractions, are doubled,
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.
