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