MathDB

Prove that every integer from

1

2019

can be represented as an arithmetic expression consisting of up to

17

symbols

2

and an arbitrary number of additions, subtractions, multiplications, divisions and brackets. The

2

's may not be used for any other operation, for example, to form multidigit numbers (such as

222

) or powers (such as

2^2

).
Valid examples:

\left((2\times 2+2)\times 2-\frac{2}{2}\right)\times 2=22 \;\;, \;\; (2\times2\times 2-2)\times \left(2\times 2 +\frac{2+2+2}{2}\right)=42

Proposed by Stephan Wagner, Austria

Problem Statement