Is Divisibility Sufficient for Proving a Product Divides Another Product?

  • Thread starter Thread starter kathrynag
  • Start date Start date
  • Tags Tags
    Abstract
kathrynag
Messages
595
Reaction score
0

Homework Statement


Show that if a | c and b | c, and (a, b) = d, then ab | cd.

Homework Equations


The Attempt at a Solution


Abstract divisibility.
We have c=am, c=bn, and d=an+bm.
 
Physics news on Phys.org
Could I multiply d=an+bm by c.
Then I have cd=acn+bcm
We have cd=c(an+bm)
cd=cd
Thus, ab | cd
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Proving differentiability for inverse function on given interval
Replies
3
Views
959
How to prove that a result does not hold in general
Replies
4
Views
2K
Relations on Sets: Need help understanding a mistake
Replies
3
Views
1K
Base 8 Logic Puzzle: Finding Solutions to Divisibility Rules
Replies
9
Views
2K
Derivative of a product of 3 terms
Replies
4
Views
1K
Does there exist a 2x2 non-singular matrix with only one 1d eigenspace?
Replies
2
Views
1K
Abstract algebra Polynomials and Prime
Replies
3
Views
1K
How can I prove that the dot product is distributive?
Replies
1
Views
2K
How to show that this expression with tensors reduces to zero?
Replies
6
Views
1K
Use greedy vertex coloring algorithm to prove the upper bound of χ
Replies
0
Views
55

Hot Threads

Recent Insights

Back
Top