Question

suppose for integers x,y we have 2x+3y is divisible by 17.prove that 9x+5y >s also divisible by 17​

Answer 1

Answer:

hope this will help you

Step-by-step explanation:

1.  9x + 5y == 0 (mod 17). Thus 9x + 5y is divisible by 17. The other implication, that if 9x + 5y is divisible by 17 then 2x + 3y is divisible by 17, can be proved in a similar fashion.

Solution. 17∣(2x+3y)⟹17|[13(2x+3y)], or 17∣(26x+39y)⟹17∣(9x+5y). Conversely, 17∣(9x+5y)⟹17∣[4(9x+5y)], or 17∣(36x+20y)⟹17∣(2x+3y).

I have a difficulty understanding how

17∣(26x+39y)

implies

17∣(9x+5y)