Timeline for Prove ${^{b}a} \equiv {^{b+1}} a \pmod {10^{\lfloor{\log_{10} (^{b}a) }\rfloor + 1}} \Rightarrow a=5$ as $a$ and $b$ are two integers greater than $1$
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 28 at 2:06 | vote | accept | Marco Ripà | ||
| May 23 at 16:19 | answer | added | John Omielan | timeline score: 2 | |
| May 21 at 1:22 | comment | added | LSpice | Re, OK, I have changed "assume" to "define". | |
| May 21 at 1:22 | history | edited | LSpice | CC BY-SA 4.0 |
Assume -> define
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| May 21 at 0:48 | comment | added | Marco Ripà | P.S. Feel free to edit the first line of text accordingly :) | |
| May 21 at 0:42 | comment | added | Marco Ripà | @LSpice Basically, I just need a compact way to write a tetration, we have the power tower a^a^...^a b-times and I invoke the standard definition of integer tetration by ruling out the base case b=1 since we are excluding it by hypothesis (otherwise we would find infinite solutions to the given congruence relation - and even if we improve the stated constraint -, such as 51, 57, 101, and so on). | |
| May 20 at 23:20 | history | edited | LSpice | CC BY-SA 4.0 |
TeX
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| May 20 at 23:17 | comment | added | LSpice | Is your sentence "Assume …" actually a definition of $^b a$, rather than an assumption about it? If not, then what is the definition? | |
| May 20 at 22:12 | comment | added | Marco Ripà | P.S. Here we are clearly assuming radix-10, just let me know if it is worth including this info in the text. | |
| May 20 at 21:46 | comment | added | Marco Ripà | I've just removed the redundant statement "10 $\nmid a$" at the beginning since it is trivial to point out that there can't be any multiple of $10$ satisfying the given congruence even if we include the $b=1$ case. I stated the aforementioned condition since this result comes from my research focused on the "congruence speed" of the integer tetration in radix-$10$, where every multiple of $10$ is not characterized by the constant congruence speed property, which involves all the other tetration bases. | |
| May 20 at 21:35 | history | edited | Marco Ripà | CC BY-SA 4.0 |
Removing redundant Hp.
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| May 20 at 21:21 | history | edited | Marco Ripà | CC BY-SA 4.0 |
typo if-->it
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| May 20 at 21:04 | history | asked | Marco Ripà | CC BY-SA 4.0 |