I don't know. About two years ago, I unintentionally found that for 3, 5 and 7 the statement is true. At first I guess it is true for all odd numbers. Then I tried for 9, 11,13, 15, and found that it is not true for 9 and 15. Then in subsequent two years I tried two more numbers 17 and 19, they are both true. Hence I guess that it is true for all prime numbers. However, I just cannot prove it.

Hello....If I Am not wrong... This is Fermat's little theorem...isn't it?