What peculiarity do the numbers 567 and 854 share that no other three-digit positive integer number has?

(In reply to Unsure about uniqueness by Syzygy)

567 and 854 are the only two 3-digit positive integers, when combined with their squares (321489 and 729316, respectively) are each composed of distinct digits 1-9.

The two 3-digit positive integers share the property with one other 3-digit positive integer, that when squared, all digits are distinct. That third number is 807. 807 and 807² (651249) comprises the distinct digits 0-9, less the digit 3.

Posted by Dej Mar on 2008-11-03 12:52:59