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'What a Coincidence!' printed from http://nrich.maths.org/
Consider the arithmetic sequences:
$1998, 2005, 2012, ...$ and
$1996, 2005, 2014, ...$
Which is the next number after $2005$ that appears in both sequences?
If you liked this problem, here is an NRICH task
which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.