What is a Lychrel number? What are its applications?
In: Mathematics
Take any natural number, lets use 175 for today. Write it in reverse: 571. Now add the two to get 175 + 571 = 746.
Okay, then do the same again, reverse and add: 746 + 647 = 1393.
And again: 1393 + 3931 = 5334.
Aaaaand one more time: 5334 + 4335 = 9669.
We now arrived at a _palindrome_, a number that looks the same if we reverse it. Does this always happen, regardless of what number we started with? It might take four or a hundred or a bazillion steps for some number to finally settle; but do all of them eventually do so? The answer is: we don’t know. So we decided to call those hypothetical numbers where this process never spits out a palindrome “Lychrel numbers”.
So we have no idea if they exist. Apart from some low amount of fame, this question is pretty inconsequential, though. It has absolutely no suspected relation to real life at all. It isn’t even important for almost anything else within mathematics.
It nonetheless is difficult problem and in trying or succeeding to solve it, we might learn new methods or grasp concepts that could help with more important things. Or we just try because we find it interesting in itself.
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