Who Knows Pythagoras?

  • Let aa be the hypotenuse of a right angled triangle; with other two sides being 55 and 1212 respectively.
  • Let bb be the sum of all positive integers which cannot be the sides of a integer-sided right angled triangle.
  • Let cc be the greatest common divisor of all possible values of xyzxyz, where xx, yy, and zz are the integral sides of a right angled triangle subject to x+y+z100x+y+z \ge 100.
  • Let dd be the number of different integer-sided right-angled triangles with one of the sides equal to 385385.

Determine a+b+c+da+b+c+d.


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