1

Part of 2008 Iran MO (2nd Round)

Problems(2)

Diagonals of a n-gon - Iran NMO 2008 - Problem1

Source:

In how many ways, can we draw

n-3

n

-gon with equal sides and equal angles such that:

i)

none of them intersect each other in the polygonal.

ii)

each of the produced triangles has at least one common side with the polygonal.

combinatorics unsolvedcombinatorics

Prove that a=1 if 4(a^n+1) is a cube for all n (Iran 2008)

Source:

\mathbb{N}

is the set of positive integers and

a\in\mathbb{N}

. We know that for every

n\in\mathbb{N}

4(a^n+1)

is a perfect cube. Prove that

a=1

number theory proposednumber theory