detailed solution

1. A primitive Pythagorean triple is an ordered tripe of integers (x, y. z) such that x+y? =2. where x, y and z are pairwisely relatively prime integers. Determine exactly 10 primitive Pythagorean triples and be able to exhibit that they satisfy the given equation. 2. Solve the system of congruence 3x + 7y = 10 ( mod 16) 5x + 2y = 9 ( mod 16) . Hint: Eliminate x by multiplying each congruence a suitable constant and then adding them to form a linear congruence containing only y as a variable. Likewise, eliminate y by multiplying each congruence a suitable constant and then adding them to form a linear congruence containing only x as a variable