Toss the grated potatoes with flour in a large bowl. Stir in mashed potatoes until combined. In a separate bowl, whisk together the egg and skim milk; mix into the potatoes. Season to taste with salt and pepper.
Heat the olive oil in a large skillet over medium-high heat. Drop in the potato mixture, forming patties about 2 inches in diameter. Fry on both sides until golden brown, 3 to 4 minutes per side. Drain on a paper towel-lined plate. Serve warm.
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