+0  
 
0
1
2309
4
avatar+1811 

Let $x$ and $y$ be integers. Show that $9x + 5y$ is divisible by 19 if and only if $x + 9y$ is divisible by 19.

 Jul 30, 2015

Best Answer 

 #1
avatar+31320 
+21

Divisible by 19?

.

.
 Jul 30, 2015
 #1
avatar+31320 
+21
Best Answer

Divisible by 19?

.

Alan Jul 30, 2015
 #2
avatar+111600 
+11

I really like this solution Alan, thank you.

For the last bit you just have to show that 9m/19 is not an integer for  0<m<19

can't you just say that 9 and 19 are relatively prime so 9m/19 will only be an integer if m is a multiple of 19.  Since m cannot be a multiple of 19, 9m/19 is not an integer.

That is, 9m is not divisable by 19.

 Jul 31, 2015
 #3
avatar+31320 
+5

"For the last bit you just have to show that 9m/19 is not an integer for  0<m<19 can't you just say that 9 and 19 are relatively prime so 9m/19 will only be an integer if m is a multiple of 19.  Since m cannot be a multiple of 19, 9m/19 is not an integer. That is, 9m is not divisable by 19"

 

Yes.  Much neater Melody.

 Aug 1, 2015
 #4
avatar+111600 
+1

Thankyou Alan  

 Aug 1, 2015

43 Online Users

avatar
avatar
avatar