MathDB

1

Part of 2021 Azerbaijan EGMO TST

Problems(2)

two numbers replaced with their product

Source: Azerbaijan EGMO TST 2021, D1 P1

8/11/2023
Let nn be an even positive integer. There are nn real numbers written on the blackboard. In every step, we choose two numbers, erase them, and replace each of them with their product. Show that for any initial nn-tuple it is possible to obtain nn equal numbers on the blackboard after a finite number of steps.
combinatoricsAZE EGMO TST
Mathematics

Source:

9/4/2020
p is a prime number, k is a positive integer Find all (p, k): k!=(p3−1)(p3−p)(p3−p2)k!=(p^3-1)(p^3-p)(p^3-p^2)
prime numbersprimenumber theoryAZE EGMO TST