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Integer right triangles

Problem 39

Published on Friday, 14th March 2003, 06:00 pm; Solved by 36358

If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120.

{20,48,52}, {24,45,51}, {30,40,50}

For which value of p ≤ 1000, is the number of solutions maximised?