Originally Posted by

**tonio** I don't see this clearly: take $\displaystyle n=2\,,\,\,a=5\,,\,7\!\!\!\pmod{256}$ . Now, there are only 6 options to get a sum that equals $\displaystyle 5\!\!\!\pmod{256}$ according to the conditions: $\displaystyle 0-5\,,\,5-0\,,\,1-4\,,\,4-1\,,\,2-3\,,\,3-2$, but there're 8 options for $\displaystyle 7\!\!\!\pmod{256}: 7-0\,,\,0-7\,,\,1-6\,,\,6-1\,,\,2-5\,,\,5-2\,,\,3-4\,,\,4-3$ , so this means the probability to obtain 5 is less than the prob. to obtain 7...or ain't so?