Your task is to perform a time complexity analysis of the two aforementioned Python functions, summarizing the time complexity of each Python function by making use of notation. Motivate the order of each Python function obtained. Given the outcome of your time complexity analysis, explain the growth in the execution time observed for each Python function when the input size changes from 1000 to 2000.

A Pythagorean triple (a,b,c) consists of three strictly positive integers a,b, and c, for which a2+ b2=c2. The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a2+b2=c2. Thus, Pythagorean triples describe the three integer side lengths of a right triangle. A well-known example of a Pythagorean triple is (3,4,5), but its multiples such as (6,8,10) and (9,12,15) are also Pythagorean triples. In general, if (a,b,c) is a Pythagorean triple, then so is (ka,kb,kc), for any positive integer k. To get all Pythagorean triples (a,b,c) for which 0