[net.math] Cyclic Integers Puzzle

aark (07/22/82)

CYCLIC INTEGERS:

The 6-digit integer 142857 has the following curious property.
When multiplied by integers from 1 to 6:

	142857 x 1 = 142857
	142857 x 2 = 285714
	142857 x 3 = 428571
	142857 x 4 = 571428
	142857 x 5 = 714285
	142857 x 6 = 857142

The products contain the same digits in the same order as 142857,
except they are circularly rotated.  For example, 285714 results
if 142857 is circularly rotated two digits to the left.

In general, an n-digit integer A is a cyclic integer if all its
multiples, A x 1 through A x n, are circular rotations of A.

THE CHALLENGE:

Find some other cyclic integers.  Hint: Zeroes are allowed anywhere,
including leading zeroes.

After a while I'll post my solution.