This is a very interesting word problem that I came across in an old textbook of mine. So I know its got something to do with primes and composities but other than that, the textbook gave no hints really and I'm really not sure about how to approach it. Any guidance hints or help would be truly greatly appreciated. Thanks in advance :) So anyway, here the problem goes:
Find the smallest positive integer that ends in $17$, is divisible by $17$, and the sum of its digits is equal to $17$.