Integers Shared by Arithmetic Sequences

Algebra Level 4

\[ \begin{array}{llllll} A_1 : & 2, & 9, & 16, \ldots , & 2 + (1000-1) \times 7 \\ A_2: & 3, & 12 , & 21, \ldots, & 3 + (1000-1) \times 9? \\ \end{array} \]

How many integers appear in both of the following arithmetic progressions above?

Details and assumptions

Since 2 appears in \(A_1\) but not in \(A_2\), it does not appear in both of the arithmetic progressions.

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