How to Prove Common Divisors Divide the G.C.D.?

lifeonfire
Messages
12
Reaction score
0

Homework Statement



Prove that for two integers m,n: all the common divisors divides the g.c.d.(m,n).

Homework Equations





The Attempt at a Solution



g.c.d = aA +bB ; where a, b are the integers

and let d be a common divisor, then:
d|a and d|b.

After this I have no clue where to go.
 
Physics news on Phys.org
Do you know the formula for gcd involving lcm? Try using that.
 
u can even try having a look at how gcd of 2 numbers is obtained http://en.wikipedia.org/wiki/Euclidean_algorithm"
 
Last edited by a moderator:

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Compute the G.C.D of two Gaussian Integers
Replies
1
Views
1K
Can anyone please review/verify this proof of greatest common divisor?
Replies
2
Views
1K
Proving the Existence of a Number with n Divisors
Replies
18
Views
2K
If ab = m(a,b), prove that m = [a,b]
Replies
16
Views
2K
Finding 5 Positive Integers with GCD Difference
Replies
6
Views
2K
Proof About Greatest Common Divisors
Replies
8
Views
2K
Prove that ##\lim\limits_{x \to \infty} f(x) = 0##
Replies
3
Views
579
Proving g.c.d.(a,b) in a PID: A Homework Solution
Replies
1
Views
2K
Nilpotent Elements of ##\mathbb{Z}/n\mathbb{Z}##
Replies
5
Views
3K
What is the Greatest Common Divisor of Two Polynomials?
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top