Substitute each of the capital letters in bold by a different base ten digit from 0 to 9 to satisfy this set of alphametic relationships. None of the numbers can contain any leading zero.
- NATE is divisible by 3, and:
- ATEN is divisible by 7, and:
- ANTE is divisible by 11, and:
- NEAT is divisible by 17.
What are the possible value(s) that NEAT