## Solution for problem 9 Chapter 12

# (a) Prove that if x, y, z is a primitive Pythagorean triple in which x and z are

Elementary Number Theory | 7th Edition

(a) Prove that if x, y, z is a primitive Pythagorean triple in which x and z are consecutivepositive integers, thenx = 2t(t + 1) y = 2t + 1 z = 2t(t + 1) + 1for some t > 0.[Hint: The equation 1 = z - x = s2 + t2 - 2st implies thats - t = l.](b) Prove that if x, y, z is a primitive Pythagorean triple in which the difference z - y = 2,thenx = 2t y = t2 - 1 z = t2 + 1for some t > 1.

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L26 - 2 Consider the graph of f(x)s kcedbel: Where is the function f(x)c ocveupanddown Test for Concavity ▯▯ Assume that f (x)e sson( a,b). 1. If f (x) > 0f oral x on (a,b), then f 2. If f (x) < 0f oral x on (a,b), then f

###### Chapter 12, Problem 9 is Solved

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(a) Prove that if x, y, z is a primitive Pythagorean triple in which x and z are