P8

Part of 2024 Bangladesh Mathematical Olympiad

Problems(2)

Bosonti n-point

Source: BdMO 2024 Secondary National P8

A set consisting of

n

points of a plane is called a bosonti

n

-point if any three of its points are located in vertices of an isosceles triangle. Find all positive integers

n

for which there exists a bosonti

n

combinatoricscombinatorial geometry

Source: BdMO 2024 Higher Secondary National P8

k

be a positive integer. Show that there exist infinitely many positive integers

n

\frac{n^n-1}{n-1}

k

distinct prime divisors.
Proposed by Adnan Sadik

number theoryprime divisorNT construction