Apoorva Khare

Maps Preserving the Sum-to-Difference Ratio

For a field F, what are all functions f:F→F that satisfy the functional equation f((x+y)/(x−y))=(f(x)+f(y))/(f(x)−f(y)) for all x≠y in F? We solve this problem for the fields Q,R, and a class of its subfields that includes the real constructible numbers, the real algebraic number...