MathDB

8

Part of 2015 Online Math Open Problems

Problems(2)

2014-2015 Spring OMO #8

Source:

4/14/2015
Determine the number of sequences of positive integers 1=x0<x1<⋯<x10=1051 = x_0 < x_1 < \dots < x_{10} = 10^{5} with the property that for each m=0,…,9m=0,\dots,9 the number xm+1xm\tfrac{x_{m+1}}{x_m} is a prime number.
Proposed by Evan Chen
Online Math Open
2015-2016 Fall OMO #8

Source:

11/18/2015
The two numbers 00 and 11 are initially written in a row on a chalkboard. Every minute thereafter, Denys writes the number a+ba+b between all pairs of consecutive numbers aa, bb on the board. How many odd numbers will be on the board after 1010 such operations?
Proposed by Michael Kural
Online Math Open