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。