MathDB

3

Part of 2021 New Zealand MO

Problems(2)

max no of golden terms in a permutation of 1, 2, 3, . . . , 2021?

Source: New Zealand MO 2021 Round 1 p3

9/20/2021
In a sequence of numbers, a term is called golden if it is divisible by the term immediately before it. What is the maximum possible number of golden terms in a permutation of 1,2,3,...,20211, 2, 3, . . . , 2021?
number theorydivisible
sum of any 3 of n is a prime, max n wanted

Source: New Zealand MO 2021 Round 2 p3 NZMO

10/6/2021
Let {x1,x2,x3,...,xn}\{x_1, x_2, x_3, ..., x_n\} be a set of nn distinct positive integers, such that the sum of any 33 of them is a prime number. What is the maximum value of nn?
number theoryprime