# Who Knows Pythagoras?

• Let $$a$$ be the hypotenuse of a right angled triangle; with other two sides being $$5$$ and $$12$$ respectively.
• Let $$b$$ be the sum of all positive integers which cannot be the sides of a integer-sided right angled triangle.
• Let $$c$$ be the greatest common divisor of all possible values of $$xyz$$, where $$x$$, $$y$$, and $$z$$ are the integral sides of a right angled triangle subject to $$x+y+z \ge 100$$.
• Let $$d$$ be the number of different integer-sided right-angled triangles with one of the sides equal to $$385$$.

Determine $$a+b+c+d$$.

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