Problem #PRU-32861

Problems Algebra and arithmetic Number theory. Divisibility Divisibility of a number. General properties Methods Examples and counterexamples. Constructive proofs

Problem

A country is called a Fiver if, in it, each city is connected by airlines with exactly with five other cities (there are no international flights).

a) Draw a scheme of airlines for a country that is made up of 10 cities.

b) How many airlines are there in a country of 50 cities?

c) Can there be a Fiver country, in which there are exactly 46 airlines?