Question

Prove that

Answer 1

if x satisfies
\[x^{n}+a_{n-1}x^{n-1}+.....+a_{0}=0\]
for some integers an-1,....,a0,then x is irrational unless x is an integer

Answer 2

the solution probably has to do with prime numbers ...the book hasnt talked about sequences yet

Answer 3

its from Spivak's Calculus Chapter 2 ...i just proved that \[\sqrt{n}\]is irrational unless n=m^2

Answer 4

for some natural number m...i think it probably depends on that

Answer 5

and it says in parentheses in that problem (Why this is a generalization of the previous problem?) that i proved the previous fact