MathDB

k,n

are two arbitrary positive integers. Prove that there exists at least

(k-1)(n-k+1)

positive integers that can be produced by

n

number of

k

's and using only

+,-,\times, \div

operations and adding parentheses between them, but cannot be produced using

n-1

number of

k

's.
Proposed by Aryan Tajmir

Problem Statement