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Mathematik-Online problems:

Problem 521: Operation Table, Axioms of Groups

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Let $ P$ be the set of all prime numbers $ \leq 13$. Define on $ P$ the binary operation $ \diamond: P\times P \longrightarrow P$, with

$\displaystyle p \diamond q =$   greatest prime factor of $\displaystyle p+q-2 \; , $


a)
Calculate the operation table of $ (P,\diamond)$.
b)
Find a solution of $ 5\diamond x=5$ in $ (P,\diamond)$, and indicate whether $ (P,\diamond)$ is a group or not.

(Authors: Höllig/Höfert)

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  automatisch erstellt am 14. 10. 2004