1. The problem statement, all variables and given/known data Let [itex] A_n [/itex] be the algebraic numbers obtained as roots of polynomials with integer coeffiecients that have degree n. Using the fact that every polynomial has a finite number of roots. Show that [itex] A_n [/itex] is countable. 3. The attempt at a solution So an nth degree polynomial has n roots. And (n+1) coefficients. so for the nth degree polynomial I will have the first coefficient go to the first prime and then the next one to the second prime and then (n+1) coefficient to the n+1 prime. And we take the absoulte value of the integers before we raise them to a prime. For example the first coefficient will go to [itex] 2^x [/itex] now to take care of the same nth degree polynomial but might have negative coefficients. we will have the first coefficient go to the (n+2) prime and then keep continuing this. We will just keep continuing this and shifting down the list of primes to make sure we got every polynomial. Will this work or Am I way off.