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Hier sind einige Aufgaben zum so genannten Grundwissen der Jahrgangsstufen 5 mit 10 zu finden.

Zusätzlich ein paar Ergänzungen und Übungen.

Ein Beispiel: Auf wie viele unterscheidbare Arten lassen sich vier (nicht unterscheidbare) rote und vier (nicht unterscheidbare) blaue Kugeln auf die acht Ecken eines Würfels verteilen?

What does factorization mean?

$26=2\cdot13$ is a complete factorization, while $1155=21\cdot55$ is a factorization, too. The latter can be extended to a complete one: $1155 = 3\cdot5\cdot7\cdot11$.

Last update: July 22, 2018

New project

I've (re-)started the factorization of the numbers 2011^64+b^64 (with b from 1 upto 2010).
According to factordb.com 928 out of the 2010 numbers are prime or completely factored, so 1082 composites are left.
This will take a while.
August 1, 2018

Part b=1: Factoring 2011^64+1 with a Septic

I used snfs with a degree 7 polynomial and got the factorization
2011^64+1 = p87 $\cdot$ p106,
where p87 = 152146267448407391878533680747587442905537546667385778069360578099894933832502467776001
and p106 = 8842294172926589105078232195561401071095188440243226829035224116157496247949043814944257660272106664445697.
The siever was 14e (with -a option), the range was 12M upto 98M.
A (shortened) logfile is available.

August 9, 2018

Part b=3: Factoring 2011^64+3^64 with a Quintic

I used snfs with a degree 5 polynomial and got the factorization
2011^64+3^64 = p59 $\cdot$ p64 $\cdot$ p83,
where p59 = 10658144630390929217054112149079128123956352658185677464193,
p64 = 9972283959763988492782175983705945168817463151921787471317484801,
and p83 = 71518343198324461820156031896306568855663425739721725978561809536957912211510668673.
A (shortened) logfile is available.

August 1, 2018