import java.util.Arrays;


public class ArrayElementShifter {

    private static boolean printDebug = true;

    private static int dimension = 10;

    private static int n = 3;

    /**
     * @param args
     */
    public static void main(String[] args) {

        //array initialization
        Integer[] initArray = new Integer[dimension];
        for(int i=0; i<dimension; i++) initArray[i] = i+1;

        //Move N elements to the end and print results
        System.out.println("\nResult: " + Arrays.toString(moveNElementsToTheEnd(initArray, n)));
    }

    public static final Object[] moveNElementsToTheEnd(Object[] initArray, int n){

        //for index calculation simplicity natural numbers (1,2,3...) are used;
        //for addressing array elements index-1 is used

        if(initArray.length % n != 0){
            int tmpIdx = 1, freeCellIdx = 1, nextValueIdx = 0;
            Object tmp = initArray[freeCellIdx -1];

            for(int i=0; i<initArray.length; i++){
                nextValueIdx = (freeCellIdx + n > initArray.length ? freeCellIdx - initArray.length : freeCellIdx) + n;
                if(nextValueIdx == tmpIdx){
                    initArray[freeCellIdx-1] = tmp;
                } else{
                    initArray[freeCellIdx-1] = initArray[nextValueIdx-1];
                }

                freeCellIdx = nextValueIdx;

                if(printDebug) {
                    System.out.println("Debug:" + Arrays.toString(initArray));
                }
            }
        } else {
            int i =0;
            while(i<n){
                Object tmp = initArray[i];
                int j=0;
                while(i+n*(j+1) < initArray.length){
                    initArray[i+n*j] = initArray[i+n*(j+1)];
                    j++;
                    if(printDebug) {
                        System.out.println("Debug:" + Arrays.toString(initArray));
                    }
                }
                initArray[i+n*j] = tmp;
                i++;
                if(printDebug) {
                    System.out.println("Debug:" + Arrays.toString(initArray));
                }
            }
        }

        return initArray;
    }
}

Dim: 10; N:3

Debug:[4, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Debug:[4, 2, 3, 7, 5, 6, 7, 8, 9, 10]
Debug:[4, 2, 3, 7, 5, 6, 10, 8, 9, 10]
Debug:[4, 2, 3, 7, 5, 6, 10, 8, 9, 3]
Debug:[4, 2, 6, 7, 5, 6, 10, 8, 9, 3]
Debug:[4, 2, 6, 7, 5, 9, 10, 8, 9, 3]
Debug:[4, 2, 6, 7, 5, 9, 10, 8, 2, 3]
Debug:[4, 5, 6, 7, 5, 9, 10, 8, 2, 3]
Debug:[4, 5, 6, 7, 8, 9, 10, 8, 2, 3]
Debug:[4, 5, 6, 7, 8, 9, 10, 1, 2, 3]

Result: [4, 5, 6, 7, 8, 9, 10, 1, 2, 3]

Dim: 13; N:3

Debug:[4, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]
Debug:[4, 2, 3, 7, 5, 6, 7, 8, 9, 10, 11, 12, 13]
Debug:[4, 2, 3, 7, 5, 6, 10, 8, 9, 10, 11, 12, 13]
Debug:[4, 2, 3, 7, 5, 6, 10, 8, 9, 13, 11, 12, 13]
Debug:[4, 2, 3, 7, 5, 6, 10, 8, 9, 13, 11, 12, 3]
Debug:[4, 2, 6, 7, 5, 6, 10, 8, 9, 13, 11, 12, 3]
Debug:[4, 2, 6, 7, 5, 9, 10, 8, 9, 13, 11, 12, 3]
Debug:[4, 2, 6, 7, 5, 9, 10, 8, 12, 13, 11, 12, 3]
Debug:[4, 2, 6, 7, 5, 9, 10, 8, 12, 13, 11, 2, 3]
Debug:[4, 5, 6, 7, 5, 9, 10, 8, 12, 13, 11, 2, 3]
Debug:[4, 5, 6, 7, 8, 9, 10, 8, 12, 13, 11, 2, 3]
Debug:[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 11, 2, 3]
Debug:[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 2, 3]

Result: [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 2, 3]

Dim: 8; N:4

Debug:[5, 2, 3, 4, 5, 6, 7, 8]
Debug:[5, 2, 3, 4, 1, 6, 7, 8]
Debug:[5, 6, 3, 4, 1, 6, 7, 8]
Debug:[5, 6, 3, 4, 1, 2, 7, 8]
Debug:[5, 6, 7, 4, 1, 2, 7, 8]
Debug:[5, 6, 7, 4, 1, 2, 3, 8]
Debug:[5, 6, 7, 8, 1, 2, 3, 8]
Debug:[5, 6, 7, 8, 1, 2, 3, 4]

Result: [5, 6, 7, 8, 1, 2, 3, 4]