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  3. exercise 2 2 1 consider the set pt of all pythagor

Exercise 2 2 1 Consider the set PT of all Pythagorean triplets For a b...

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Algebra

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Exercise 2 2 1 Consider the set PT of all Pythagorean triplets For a b c PT we assume a bc Then V a b c PT a b c 60 a b c 60 a b c 3 4 5 Hint Prove that for every a b c PT we have that 3 a b and that 5 a b c Conclude that 60 a b c Observe also that a b c 30 a b c 3 4 5 2 Prove that if a b c E PT is such that a b c form an arithmetic progression then a b c 3k 4k 5k for some k N 0 Conclude that 3 4 5 is the only PPT whose components form such a progression

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