Timeline for Characterizing $x y \equiv r \pmod{a^n}$ when $a^{n-1} \leq x, y < a^n$
Current License: CC BY-SA 4.0
4 events
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| Apr 11, 2020 at 7:49 | comment | added | Mak Nazečić-Andrlon | @GerryMyerson Indeed, almost all appear. These are the exceptions I've found, written as $f(a, n)$: $f(2, 2) = \{3\}$, $f(2, 3) = \{5, 7\}$, $f(2, 4) = \{11, 13\}$, $f(2, 5) = \{19, 29\}$. They're primes, which makes sense that some should appear. But for higher $a$ or $n$, it seems to always come up with every possible $r$. | |
| Apr 11, 2020 at 5:08 | comment | added | Gerry Myerson | Since the number of $x,y$ pairs greatly exceeds $a^n$, I would expect most values of $r$ to appear as remainders. Have you tried any experiments? Say, $32\le x,y<64$? | |
| Apr 11, 2020 at 2:45 | history | edited | Mak Nazečić-Andrlon | CC BY-SA 4.0 |
added 6 characters in body
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| Apr 11, 2020 at 2:38 | history | asked | Mak Nazečić-Andrlon | CC BY-SA 4.0 |