In a small saucepan, cover peeled potatoes with water. Bring water to a boil and cook until tender, about 15 minutes. Let cool and mash.
In a large bowl, mix together salmon, egg, potatoes, salt and pepper. Mold the mixture into patties (whatever size you choose). Coat both sides of the patties with flour.
Heat oil over a medium-high heat in a large skillet. Fry the patties (2 or 3 at a time) on both sides until golden brown. Drain on paper towels before serving.