# abstract algebra proof

• Jan 27th 2010, 01:22 PM
Deepu
abstract algebra proof
a)let a be a positive integer.If square root of a is rational, prove that square root of a is an integer.

b)let r be a rational number and a an integer such that r^n = a .Prove that r is an integer.

• Jan 27th 2010, 02:47 PM
hatsoff
Quote:

Originally Posted by Deepu
a)let a be a positive integer.If square root of a is rational, prove that square root of a is an integer.

This is proved here:

Quadratic irrational - Wikipedia, the free encyclopedia

Quote:

b)let r be a rational number and a an integer such that r^n = a .Prove that r is an integer.
Let $r=\frac{p}{q}$, reduced. Then $q^n\big|p^n$ and so $q\big|p$. So $r\in\mathbb{Z}$.