There are 16 primitive Pythagorean triples of numbers up to 100:
(3, 4, 5) (5, 12, 13) (8, 15, 17) (7, 24, 25)
(20, 21, 29) (12, 35, 37) (9, 40, 41) (28, 45, 53)
(11, 60, 61) (16, 63, 65) (33, 56, 65) (48, 55, 73)
(13, 84, 85) (36, 77, 85) (39, 80, 89) (65, 72, 97)
Other small Pythagorean triples such as (6, 8, 10) are not listed because they are not primitive; for instance (6, 8, 10) is a multiple of (3, 4, 5).
So I guess 3,4,5 are the only ones that work for dates. So the next one is 9/16/2125. I guess we won't be around for it, alas. Maybe your kids or grandkids will see it!
3,4,5 is special also, of course, because it's consecutive numbers. Yeah!