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Place potatoes in a medium-sized saucepan covered 2 inches by salted water. Bring to a boil and cook until tender, about 10 minutes.
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Meanwhile in a small saucepan, combine olive oil, garlic, red pepper flakes, capers, lemon, and red onion. Bring to a simmer and remove from the heat.
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Drain the potatoes, halve lengthwise, and toss with warm dressing, celery, and parsley. Salt to taste and serve warm.
