I want to find 10 digit numbers with no repeat digits, for example:
1123456789 //fail, there are two 1\'s 6758951230 //fail, there are two 5\'s 6789012345 //
This regex works:
^(?!.*(.).*\1)\d{10}$
This uses an anchored negative look ahead with a back reference to assert that there are no repeating characters.
See a live demo working with your examples.
In java:
if (str.matches("^(?!.*(.).*\\1)\\d{10}")) // number passes