Show if $\frac{x}{y}$, with $x, y$ coprime integers, is a root of $f(T)$, then $x$ divides $a_i$ and $y$ divides $a_n$
119991
Why Rational Root Theorem requires integer coefficient polynomials?
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
100515
Prove that if $d$ divides $n$ then $φ(d)$ divide $φ(n)$ for $φ$ denotes Euler’s φ-function.
90273
Primitive roots of the unity in $\mathbb C$
113248
Proving $r!$ divides the product of r succesive positive integers
109760
Showing that the product of all $n$th Roots of Unity is $(-1)^{n+1}$
14648
Show that $f_0 - f_1 + f_2 - \cdots - f_{2n-1} + f_{2n} = f_{2n-1} - 1$ when $n$ is a positive integer
78471
Closure of $\{\frac{1}{n}\}:=M$
83036
f(g(x)) has a degree divisible by n
112709
$\frac{1}{x-a} + \frac{1}{x-b} + \frac{1}{x-c} = 0 $ has precisely two real roots
118161
Proof of dividing fractional expressions
112430
Prove that sequence $ x_{(n+1)}= \frac {a}{1+x_n}$ is convergent to positive root of $x^2+x-a=0,$where $a >0$ and $x_1 >0$
7802
Showing $\prod\limits_{i<j} \frac{x_i-x_j}{i-j}$ is an integer
107765
Prove that there exists two roots in $[-1,1]$
21891
If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
69067
Principal $n$th root of a complex number
118916
How do I prove that a polynomial F[x] of degree n has at most n roots