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Peel potatoes and boil until fork tender.
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Drain well; return to saucepan over low heat. Add butter; mash potatoes well. Stir in flour and salt.
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Gather mixture into a ball; turn onto lightly floured surface.
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Knead lightly until smooth. Divide dough in half.
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Roll out one half into an 8 inches (20 cm) circle, about 1/4 inches thick. Cut into quarters; set aside.
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Repeat with remaining dough.
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In large nonstick skillet, heat half the oil over medium-high heat.
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Cook dough quarters in batches, 2 minutes on each side or until golden brown, adding more oil as necessary.
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Serve warm.