Abstract: It is well known that primes of the form 4k+1 and primes of the form 4k+3 behave quite differently, at least in some aspects. Some of these differences follow from the properties of quadratic characters (e.g., they depend on whether the character is even or odd). We shall illustrate this phenomenon by one more example related to certain determinants. In particular, for primes p=4k+1 the formulas obtained can be viewed as determinantal expressions for the class number formula for real quadratic fields.
