MathDB

For all natural

n

, an

n

-staircase is a figure consisting of unit squares, with one square in the first row, two squares in the second row, and so on, up to

n

squares in the

n^{th}

row, such that all the left-most squares in each row are aligned vertically. Let

f(n)

denote the minimum number of square tiles requires to tile the

n

-staircase, where the side lengths of the square tiles can be any natural number. e.g.

f(2)=3

and

f(4)=7

. (a) Find all

n

such that

f(n)=n

. (b) Find all

n

such that

f(n) = n+1

Problem Statement