From Albert Beiler, Recreations in the Theory of Numbers (1964):

1 + 4 + 5 + 5 + 6 + 9 = 3 + 2 + 3 + 7 + 8 + 7

Pair each digit on the left with one on the right (for example, 13, 42, 53, 57, 68, 97). The sum of these six numbers will always equal its mirror image:

13 + 42 + 53 + 57 + 68 + 97 = 79 + 86 + 75 + 35 + 24 + 31

This works for all 720 possible combinations.

Most remarkably, you can square every term in these equations and they still hold:

13² + 42² + 53² + 57² + 68² + 97² = 79² + 86² + 75² + 35² + 24² + 31²