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O ecuatie cu partea fractionara si partea intreaga
Posted: Sun Mar 16, 2008 1:16 am
by Marius Dragoi
Daca \( p \) este un numar prim fixat, sa se rezolve ecuatia:
\( p\left\{ x \right\} = x + \left\[ x \right\] \).
Posted: Tue Mar 18, 2008 1:56 pm
by Marius Dragoi
Avem:
\( p \left\{ x \right\} =x + \left\[ x \right\] \Leftrightarrow p(x- \left\[ x \right\] ) =x+ \left\[ x \right\] \Leftrightarrow x={\frac {p+1}{p-1}}{\left\[ x \right\]} \). Atunci
\( x= \frac {k(p-1)}{p} \) unde
\( k \in Z \).
Toate numerele de aceasta forma verifica ecuatia.
