1979 Yugoslav Team Selection Test

Part of Serbia Team Selection Test

Subcontests

(2)

1

marking points on a circle, venn configuration

There are two circles of perimeter

1979

1979

points be marked on the first circle, and several arcs with the total length of

1

on the second. Show that it is possible to place the second circle onto the first in such a way that none of the marked points is covered by a marked arc.

1

n s.t. gcd(m,n)=1->n prime

Find all integers

n

1<n<1979

having the following property: If

m

is an integer coprime with

n

1<m<n

m

is a prime number.