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A371556
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Table read by rows: row n is the unique primitive Pythagorean quadruple (a,b,c,d) such that (a + b + c - d)/2 = 2^n - 1 and a = b = 2^n.
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2
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4, 4, 7, 9, 8, 8, 31, 33, 16, 16, 127, 129, 32, 32, 511, 513, 64, 64, 2047, 2049, 128, 128, 8191, 8193, 256, 256, 32767, 32769, 512, 512, 131071, 131073, 1024, 1024, 524287, 524289, 2048, 2048, 2097151, 2097153, 4096, 4096, 8388607, 8388609, 8192, 8192, 33554431, 33554433, 16384, 16384, 134217727, 134217729
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OFFSET
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2,1
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COMMENTS
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A Pythagorean quadruple is a quadruple (a,b,c,d) of positive integers such that a^2 + b^2 + c^2 = d^2 with a <= b <= c. Its inradius is (a+b+c-d)/2, which is a positive integer.
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REFERENCES
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Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2024.
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LINKS
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FORMULA
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Row n = (a, b, c, d) = (2^n, 2^n, 2^(2n - 1) - 1, 2^(2n - 1) + 1).
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EXAMPLE
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Table begins:
n=2: 4, 4, 7, 9;
n=3: 8, 8, 31, 33;
n=4: 16, 16, 127, 129;
n=5: 32, 32, 511, 513;
n=6: 64, 64, 2047, 2049;
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MATHEMATICA
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cuaternas={}; Do[cuaternas=Join[cuaternas, {2^n, 2^n, 2^(2n-1)-1, 2^(2n-1)+1}], {n, 2, 35}]; cuaternas
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CROSSREFS
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KEYWORD
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nonn,easy,tabf
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AUTHOR
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STATUS
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approved
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