MathDB

Marjorie is the drum major of the world's largest marching band, with more than one million members. She would like the band members to stand in a square formation. To this end, she determines the smallest integer

n

such that the band would fit in an

n \times n

square, and lets the members form rows of

n

people. However, she is dissatisfied with the result, since some empty positions remain. Therefore, she tells the entire first row of

n

members to go home and repeats the process with the remaining members. Her aim is to continue it until the band forms a perfect square, but as it happens, she does not succeed until the last members are sent home. Determine the smallest possible number of members in this marching band.

Problem Statement