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Pythagoras stated that there exist positive natural numbers, $a$, $b$ and $c$ such that $a^2+b^2=c^2$. These three numbers, $a$, $b$ and $c$ are collectively known as a Pythagorean triple. For example, $(8, 15, 17)$ is one of these triples as $8^2 + 15^2 = 64 + 225= 289 = 17^2$. Other examples of this triple are $(3, 4, 5)$ and $(5, 12, 13)$.

Using Proof by Contradiction, show that: If $(a, b, c)$ is a Pythagorean triple, then $(a+1, b+1, c+1)$ is not a Pythagorean triple.

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    Welcome to math.SE. Since you're new here, let me give you a few pieces of advice. For one, you are asking us for help, not giving us an assignment. It would be nice if you formulated your question to reflect that fact. Second, tell us where you're stuck. That way you help us help you understand better.2012-11-17
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    yes..sorry,my bad2012-11-17
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    excuse me,can you give me sample answer for this question?urgent2012-11-17
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    You've got two answers already, niki.2012-11-17
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    More generally, if (a,b,c) is a Pythagorean triple and k is a positive integer, then (a+k,b+k,c+k) is not a Pythagorean triple.2012-11-17

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