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Benedict Irwin edited The 90 Thing.tex
over 9 years ago
Commit id: d015650d4b7ea8512c9fed82497675cc557cedf7
deletions | additions
diff --git a/The 90 Thing.tex b/The 90 Thing.tex
index fc89ad3..332945b 100644
--- a/The 90 Thing.tex
+++ b/The 90 Thing.tex
...
n & prime? & num & fac\\
0 & 0 & 1 & 1 \\
1 & 0 & 91 & 7×13\\
2 & 1 &
9091 (90;2)+1 &
9091 (90;2)+1 \\
3 & 1 & (90;3)+1 & (90;3)+1 \\
4 & 0 & ... & 7×13×19×52579 \\
5 & 0 & ... & 11×23×4093×8779 \\
...
14 & 0 & ... & 59×154083204930662557781201849 \\
15 & 1 & (90;15)+1 & (90;15)+1 \\
16 & 0 & ... & 7×11×13×23×4093×8779×599144041×183411838171 \\
17 & 0 & ... & 9091×909091×4147571×265212793249617641 \\
18 & 0 & ... & 7253×422650073734453×296557347313446299 \\
19 & 0 & ... & 7×13^2×157×859×6397×216451×1058313049×388847808493 \\
20 & 0 & ... & 2670502781396266997×3404193829806058997303 \\
21 & 0 & ... & 57009401×2182600451×7306116556571817748755241 \\
22 & 0 & ... & 7×13×19×211×241×2161×9091×29611×52579×3762091×8985695684401 \\
\end{array}
\end{equation}
we can see that if $n-1 =
3m\in\mathbb{Z}$, 3m\in\mathbb{Z^0}$, the number is divisible by
$7×13=91=(90;1)+1$\\ $7×13=(90;1)+1$\\
we can see that if $n-2 = 5m\in\mathbb{Z^0}$, the number is divisible by $(90;2)+1$\\
we can see that if $n-3 = 7m\in\mathbb{Z^0}$, the number is divisible by $(90;3)+1$\\
we can see that if $n-4 = 9m\in\mathbb{Z^0}$, the number is divisible by $(90;4)+1$\\
If we extrapolate this relationship, we have if $n-q = (1+2q)(m\in\mathbb{Z^0})$, then $(90;n)+1/((90;q)+1) \in \mathbb{Z}$.