Cate paralelograme exista in Z_p x Z_p ?

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Francisc
Euclid
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Joined: Thu Oct 04, 2007 9:36 am
Location: Timisoara

Cate paralelograme exista in Z_p x Z_p ?

Post by Francisc »

In multimea \( \mathbb{Z}_p \times \mathbb{Z}_p \), unde p este un numar prim, definim o dreapta ca fiind multimea \( \{( x, y ) \in \mathbb{Z}_p \times \mathbb{Z}_p | ax + by + c = 0,\ a, b, c \in \mathbb{Z}_p \} \). Panta unei drepte \( ax + by + c =0 \) este \( -ab^{ - 1} \in \mathbb{Z}_p \). Spunem ca doua drepte sunt paralele daca au pantele egale. Cate paralelograme exista in \( \mathbb{Z}_p \times \mathbb{Z}_p \) ?
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