I was messing around with exponential numbers and I found that the end increase from one exponential to the next is the number it was exponentiated to taken to its factorial. Is this new or is this a problem that someone can explain to me? PS:sorry about the bad handwriting I am still in middle school.
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SKYLER BALCH
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4Ha! You've discovered the same thing when I played around with Fermat's Last Theorem as a kid: The $n$th differences of $n$th powers are $n!$ This can be proven through induction. – Brian Tung Oct 08 '24 at 18:57
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I didn't prove FLT as a ten-year-old, as many of you may recall. – Brian Tung Oct 08 '24 at 18:57
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2This question is similar to: $\Delta^ny = n!$ , difference operator question.. If you believe it’s different, please [edit] the question, make it clear how it’s different and/or how the answers on that question are not helpful for your problem. Found using an Approach0 search. Note that each of your initial groups of values are of the form of $y=x^n$. Also, welcome to Math SE. – John Omielan Oct 08 '24 at 19:18