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Math / Discrete Mathematics and Its Applications 7 / Chapter 1.8 / Problem 32E

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

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Prove that there are infinitely many solutions in positive

Chapter 8, Problem 32E

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QUESTION:

Problem 32E

Prove that there are infinitely many solutions in positive integers x, y, and z to the equation x2 +y2 = z2. [Hint: Let x = m2 – n2, y = 2mn, and z = m2 + n2, where m and n are integers.]

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QUESTION:

Problem 32E

Prove that there are infinitely many solutions in positive integers x, y, and z to the equation x2 +y2 = z2. [Hint: Let x = m2 – n2, y = 2mn, and z = m2 + n2, where m and n are integers.]

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Step 1:

Here the objective is to prove that there are infinitely many solutions in positive integers x,y,z to the equation ${x}^{2}+{y}^{2}={z}^{2}$

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