4

Part of 2020 Swedish Mathematical Competition

Problems(1)

n-gon with sides 1,2,3,.., n and vertices at lattice points

Source: 2020 Swedish Mathematical Competition p4

Which is the least positive integer

n

for which it is possible to find a (non-degenerate)

n

-gon with sidelengths

1, 2,. . . , n

, and where all vertices have integer coordinates?

geometrycombinatorial geometrylatticepolygon