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def get_all_solutions_fixing_b(b): if b == 0: return 'All N' solutions = {0} for k in range(b//2+1, 2*b+1): r = (2*b-k)*k/(2*k-b) r = int(r) if int(r) == r else None if r is not None: solutions.add(r) return [(a, b) for a in sorted(solutions)] print(get_all_solutions_fixing_b(5)) # [(0, 5), (5, 5), (8, 5), (21, 5)] print(get_all_solutions_fixing_b(8)) # [(0, 8), (3, 8), (5, 8), (8, 8), (15, 8)] print(get_all_solutions_fixing_b(11)) # [(0, 11), (11, 11), (35, 11), (96, 11)] print(get_all_solutions_fixing_b(0)) # All N
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