In a blackboard there are K circles in a row such that one of the numbers 1,...,K is assigned to each circle from the left to the right.
Change of situation of a circle is to write in it or erase the number which is assigned to it.At the beginning no number is written in its own circle.
For every positive divisor d of K ,1≤d≤K we change the situation of the circles in which their assigned numbers are divisible by d,performing for each divisor d K changes of situation.
Determine the value of K for which the following holds;when this procedure is applied once for all positive divisors of K ,then all numbers 1,2,3,...,K are written in the circles they were assigned in. combinatorics unsolvedcombinatorics