Let a and b be integers. Show that 29 divides 3a+2b if and only if it divides 11a+17b.
I am unable to solve this
Am I correct in interpreting this as : "If 3a+2b is divisible by 29 then prove that 11a+17b is also divisible by 29." ?
What is an intuitive way to solve this ?
P.S : Peter Winkler has released his book, Mathematical puzzles for free. Here is the link to it : https://math.dartmouth.edu/news-resources/electronic/puzzlebook/index.php