hw5 - integer m such that m 2 = n . Prove that there is no...

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(1) Prove that for any natural n we have 10 32 n +9 7(mod 17). (2) Prove that 2 + 3 and 2 + 3 2 are irrational. (3) Show that the equation 4 x 2 - 5 y 2 = 2 has no rational solutions. Hint: reduce the equation to an equation in integers and consider it mod m for an appropriate m . (4) Let n be an integer which is not a complete square, i e there is no
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Unformatted text preview: integer m such that m 2 = n . Prove that there is no rational x such that x 2 = n . Extra Credit. To be written up and submitted separately. Prove that q 1 2 + q 2 3 + q 3 6 is irrational for any rational numbers q 1 ,q 2 ,q 3 unless q 1 = q 2 = q 3 = 0. 1...
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