Math Notes

Turn each of these palindromes “inside out” and their sum remains the same:

13031 + 42024 + 53035 + 57075 + 68086 + 97079 = 31013 + 24042 + 35053 + 75057 + 86068 + 79097

Remarkably, this holds true even if you square or cube them:

130312 + 420242 + 530352 + 570752 + 680862 + 970792 = 310132 + 240422 + 350532 + 750572 + 860682 + 790972

130313 + 420243 + 530353 + 570753 + 680863 + 970793 = 310133 + 240423 + 350533 + 750573 + 860683 + 790973

From Albert Beiler, Recreations in the Theory of Numbers, 1964.