Palindrome Equations

Comedian Demetri Martin wrote a 224-word poem that is a palindrome. That is, if you remove all spaces and punctuation, the string of letters reads the same forward as it does backward.

When I heard about this, I started thinking about palindrome equations—if you remove all the operators (e.g., +, - ×, ÷, etc.), the number string reads the same forward as it does backward. Turns out, it’s easy to make palindrome equations. For example:
  • 0 + 0 = 0 × 0
  • 1 + 2 – 3 = 3 – 2 – 1
  • 122 = 2 ÷ 2 ÷ 1
The first form can be made arbitrarily long, just by adding more 0’s. Also, it’s not that hard to make palindromes using large numbers:

0 × 12,345,543,211,234,554,321 = 1,234,554,321 – 1,234,554,321 + 0

So, creating palindrome equations is not particularly tough. Nonetheless, I decided to create some that weren’t trivial—they don’t involve multiplying or dividing by 1 or adding or subtracting 0. Here are some basic multiplication equations (the numeric palindrome is shown in parentheses):
  • 126 = 6 × 21 (126621)
  • 441 × 184 = 81,144 (44118481144)
  • 2,102,540 = 1045 × 2012 (210254010452012)
  • 2803 × 3294 = 9,233,082 (280332949233082)
Then, I decided to branch out into more complicated forms. Like fractions:
  • 25/8 = 5/8 + 5/2 (2585852)
  • 34/13 - 51/33 = 153/143 (34135133153143)
  • 4/17 + 19/42 = 491/714 (4171942491714)
  • 722/45 = 88/5 - 42/27 (722458854227)
And powers:
  • 52 × 2 = 52 + 25 (5225225)
  • 74 × 27,356 = 65,665,372 + 47 (74273566566537247)
  • 53,240 × 43 = 55 + 3,404,235 (5324043553404235)
  • 7538 × 42 = 42,483 + 57 (7538424248357)
No luck yet on a 224-term palindrome equation.