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Use the Fundamental Theorem of Arithmetic [Any integer n greater-(Answered)

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  1. Use the Fundamental Theorem of Arithmetic [Any integer n greater than one can be factored uniquely as a product of primes n = P1 x P2 x P3 x ? x Pk where P1 <= P2 <= P3 <= ?<= Pk] to prove two other theorems: a.) If p is prime, then ?P is irrational.
    (Hint: Assume that ?P is rational. Then use the fact that if k > 1, then k2 has an even number of prime factors.b.) If n is a positive integer, the ?n is either an integer or is irrational.

 

Paper#9255896 | Written in 27-Jul-2016

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