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Distinct Lines

Problem 388

Published on Saturday, 9th June 2012, 02:00 pm; Solved by 325

Consider all lattice points (a,b,c) with 0 ≤ a,b,c ≤ N.

From the origin O(0,0,0) all lines are drawn to the other lattice points.
Let D(N) be the number of distinct such lines.

You are given that D(1 000 000) = 831909254469114121.

Find D(1010). Give as your answer the first nine digits followed by the last nine digits.