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Problem 388


Problem 388


Distinct Lines

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.


不同的直线

考虑所有满足0 ≤ a,b,c ≤ N的格点(a,b,c)。

从原点O(0,0,0)引直线穿过其它格点。
记D(N)为所有不同直线的数目。

已知D(1 000 000) = 831909254469114121。

求D(1010),将其前九位数字和后九位数字作为你的答案。