MathDB

Some positive integers are initially written on a board, where each

2

of them are different. Each time we can do the following moves: (1) If there are 2 numbers (written in the board) in the form

n, n+1

we can erase them and write down

n-2

(2) If there are 2 numbers (written in the board) in the form

n, n+4

we can erase them and write down

n-1

After some moves, there might appear negative numbers. Find the maximum value of the integer

c

such that: Independetly of the starting numbers, each number which appears in any move is greater or equal to

c

4