Mix potatoes, eggs, and flour in a bowl (I squish it together with my hands). If the potatoes are not sticky enough to form a patty add a little more flour.
Form into patties.
Place oil in the skillet, enough to lightly cover the bottom of the skillet, and add 2 tablespoons butter, heat to medium-high.
Fry patties in hot oil/butter until golden brown. Serve warm.
Notes
Use 2 eggs regardless even if you are using less than 4 cups of mashed potatoes. It will help bind the patties.