If x and y are positive integers, find the number of solution of the equation 3x + 5y = 1008
+9519 Lemma: If (x, y) is a solution to the equation 3x + 5y = 1008, where x and y are positive integers, then (x + 5, y - 3) is also a solution.
Proof: 3(x + 5) + 5(y - 3) = 3x + 15 + 5y - 15 = 3x + 5y = 1008.
By trial and error, we know that (1, 201) is a solution.
By Lemma, (6, 198), (11, 195), (16, 192), etc. are all solutions.
It is easy to know that (331, 3) is a solution.
The problem simplifies to "Finding the number of multiples of 3 among (3, 6, 9, 12, ..., 201)".
The rest is trivial.
Ans: 67
