Pythagorean Quadruple

Given four points, check whether they form Pythagorean Quadruple. 
It is defined as a tuple of integers a, b, c, d such that . They are basically the solutions of Diophantine Equations. In the geometric interpretation it represents a cuboid with integer side lengths |a|, |b|, |c| and whose space diagonal is |d| . 
 

👁 Image

The cuboids sides shown here are examples of pythagorean quadruples. 
It is primitive when their greatest common divisor is 1. Every Pythagorean quadruple is an integer multiple of a primitive quadruple. We can generate the set of primitive pythagorean quadruples for which a is odd can be generated by formula :
 

a = m² + n² - p² - q², 
b = 2(mq + np), 
c = 2(nq - mp), 
d = m² + n² + p² + q²

where m, n, p, q are non-negative integers with greatest common divisor 1 such that m + n + p + q are odd. Thus, all primitive Pythagorean quadruples are characterized by Lebesgue's identity.
 

(m² + n² + p² + q²)² = (2mq + 2nq)² + 2(nq - mp)² + (m² + n² - p² - q²)m² + n² - p² - q²

 

Output: 

Yes

Time Complexity: O(1) 
Auxiliary Space: O(1)

References 
Wiki 
mathworld