MathDB
Circling Positive Integers

Source:

September 8, 2024
number theory2024

Problem Statement

Let N2N_2 be the answer to problem 2.
On a number line, Tanya circles the first \ell positive integers. Then, starting with the greatest number in the most recent circle, she circles the next \ell positive integers, so that the two circles have exactly one number in common; she repeats this until N2N_2 is in a circle. Compute the sum of all possible values of \ell for which N2N_2 is the greatest number in a circle.