2

Part of 2023 Chile National Olympiad

Problems(1)

visible lattice points on 3D from the origin x_i = 1,...,30

Source: 2023 Chile NMO L2 P2

In Cartesian space, let

\Omega = \{(a, b, c) : a, b, c

are integers between

1

30\}

\Omega

is said to be visible from the origin if the segment that joins said point with the origin does not contain any other elements of

\Omega

. Find the number of points of

\Omega

that are visible from the origin.

analytic geometrycombinatoricscombinatorial geometrylattice points