Homework Statement
We know that the gcd of two polynomials can be written as
gcd(p(x),q(x))=p(x)m(x) + q(x)n(x) for some n(x) and m(x) in F[x] F a fieldI want to show gcd(n(x),m(x))=1 for a fixed gcd(p(x),q(x))
The Attempt at a Solution
Well, what I tried was to let D(x)=gcd(p(x),q(x))...
{SOLVED}Number theory/ divisibility
Show that m^2 is divisible by 3 if and only if m is divisible by 3.
MY attempt:
I assumed that 3k=m for some integers k and m.
squared both sides and now get.
3n=m where n=3*(3k^2). Thus 3|m^2
Now the problem is when i assume:
3k=m^2 and need...
Thanks for helping!
I solved it by using the fact that (1-1/50)^(-1/2)=squareroot(50/49)=1+1/(2*50) + 1*3/(2*4*5*50^2)+1*3*5/(1*2*3*50^3)
Then 5*squareroot(2)/7=(1+1/100+1*3/(100*200)+1*3*5/(100*200*300))
[SOLVED] prove the formula of squareroot 2
Verify the following formula:
Squareroot (2)=7/5*(1+ 1/100 + 1*3/(100*200) + 1*3*5/(100*200*300) + etc..)
Use the Fact that 50=5^2*2=7^2+1
Theorem: (1+x)^a=1 +a*x/1 + (a(a-1)*x^2)/(1*2)+ (a(a-1)(a-2)*x^3)/(1*2*3)+ etc...
Hint: use the...