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EXAMPLE
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6916 is the first middle side belonging to 2^3=8 arithmetic triangles, viz., (3485,6916,10347), (3747,6916,10085), (4133,6916,9699), (4299,6916,9533), (4827,6916,9005), (5045,6916,8787), (5333,6916,8499), (6267,6916,7565) of common differences 3431, 3169, 2783, 2617, 2089, 1871, 1583, 649 respectively and integral areas. (Perimeter is obviously three times middle side and hence the same for all the triangles.)
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