The number of terms common to both the arithmetic progressions \(2, 5, 8, 11, ..., 179\) and \(3, 5, 7, 9, ..., 101\) is

Common terms are = 2 mod 3 and odd, i.e. = 5 mod 6: 5, 11, ..., 101 (limited by second AP). 5 + 6k <= 101 gives k = 0..16, 17 terms.