A Pythagorean quadruple is a set of positive integers a, b, c, and d that satisfy a^2 + b^2 + c^2 = d^2. For positive even a and b, there exist such integers c and d; for positive odd a and b, no such integers exist. Examples of primitive Pythagorean quadruples include (1, 2, 2, 3), (2, 3, 6, 7), (4, 4, 7, 9), (1, 4, 8, 9), (6, 6, 7, 11), and (2, 6, 9, 11). Oliverio gives the following generalization of this result. Let S = (a_1, ..., a_(n - 2)), where a_i are integers, and let T be the number of odd integers in S.
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