15

Part of 2023 Durer Math Competition Finals

Problems(2)

12-sided convex polygon-shaped pizza.

Source: (2022-) 2023 XVI 16th Dürer Math Competition Finals Day 2 E15

Csongi bought a

12

-sided convex polygon-shaped pizza. The pizza has no interior point with three or more distinct diagonals passing through it. Áron wants to cut the pizza along

3

diagonals so that exactly

6

pieces of pizza are created. In how many ways can he do this? Two ways of slicing are different if one of them has a cut line that the other does not have.

geometrycombinatoricscombinatorial geometry

biggest positive integer which divides p^4 - q^4

Source: (2022-) 2023 XVI 16th Dürer Math Competition Finals Day 2 E+15

What is the biggest positive integer which divides

p^4 - q^4

p

q

10

number theorydivides