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find a positive integer n so that 40n is a fifth power (of an integer) 500n is a sixth power, and 200n is a seventh power, or explain why it is impossible to do so (hint: let x = e2(n) and y = e5(n) use the given assumptions about n to find systems of linear congruences that x and y must satisfy. you may leave n in terms of its canonical prime factorization. show as much work as possible

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# Need desparate help on this question concerning finding a positive integer

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