Saturday, July 6, 2019

polynomials - sum of square root of primes 2

I dont know how to solve the problem below.



(1) p[1], p[2], , p[n] are distinct primes, where n=1,2,

Let a[n] be the sum of square root of those primes, that is, a[n]=p[1]++p[n]. Show that there exists a polynomial with integer coefficients that has a[n] as a solution.



(2) Show that a[n] is irrational.



I can solve this without using (1) for (2). But my teacher said (1) is a hint for (2).
Help please?

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