12

Part of 2006 Stanford Mathematics Tournament

Problems(2)

Largest Prime Factor

Source:

What is the largest prime factor of 8091?

number theoryprime factorizationalgebradifference of squaresspecial factorizations

2006 SMT Team Round #12 - Number of k-tuples

Source:

Find the total number of

k

(n_1,n_2,...,n_k)

of positive integers so that

n_{i+1}\ge n_i

i

k

regular polygons with numbers of sides

n_1,n_2,...,n_k

respectively will fit into a tesselation at a point. That is, the sum of one interior angle from each of the polygons is

360^{\circ}