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

 Sep 4, 2018
 #1
avatar+4396 
+1

if direction

assume (x+9y) is divisible by 19.

 

x+9y = 19k

 

9x+5y = 9(19k-9y)+5y =

19(9k) - 76y =

19(9k - 4y)

 

and thus we see (9x+5y) is divisible by 19

 

you try the only if direction

 Sep 4, 2018
 #2
avatar+95 
+3

thanks

 Sep 5, 2018

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