MathDB

20

Part of 2016 Online Math Open Problems

Problems(2)

2015-2016 Spring OMO #20

Source:

3/29/2016
Define A(n)A(n) as the average of all positive divisors of the positive integer nn. Find the sum of all solutions to A(n)=42A(n)=42.
Proposed by Yannick Yao
Online Math Open
2016-2017 Fall OMO Problem 20

Source:

11/16/2016
For a positive integer kk, define the sequence {an}n≥0\{a_n\}_{n\ge 0} such that a0=1a_0=1 and for all positive integers nn, ana_n is the smallest positive integer greater than an−1a_{n-1} for which an≡kan−1(mod2017)a_n\equiv ka_{n-1}\pmod {2017}. What is the number of positive integers 1≤k≤20161\le k\le 2016 for which a2016=1+(20172)?a_{2016}=1+\binom{2017}{2}?
Proposed by James Lin