- #1
evinda
Gold Member
MHB
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Hi! (Nerd)
I have to find the values $w_p(x)$ and $|x|_p$ for $x=\frac{3}{686}$ and $x=\frac{56}{12}$ for $p=7,5$.
That's what I have tried:
Could you tell me if it is right or if I have done something wrong? (Thinking)
I have to find the values $w_p(x)$ and $|x|_p$ for $x=\frac{3}{686}$ and $x=\frac{56}{12}$ for $p=7,5$.
That's what I have tried:
- $$x=\frac{3}{686}=\frac{3}{2 \cdot 7^3}=3 \cdot 2^{-1} \cdot 7^{-3} $$
$$p=7: x=7^{-3} \cdot 3 \cdot 2^{-1} \mapsto 7^3=343= \left |\frac{3}{686} \right|_7$$
$$w_7 \left ( \frac{3}{686}\right)=-3$$
$$p=5: x=5^0 \cdot 7^{-3} \cdot 3 \cdot 2^{-1} \mapsto 5^{-0}=1=\left |\frac{3}{686} \right |_5$$
$$w_5 \left ( \frac{3}{686}\right)=0$$
$$$$ - $$x=\frac{56}{12}=2 \cdot 7 \cdot 3^{-1} $$
$$p=7: x=7^1 \cdot 2 \cdot 3^{-1} \mapsto 7^{-1}=\frac{1}{7}=\left |\frac{56}{12} \right |_7$$
$$w_7 \left ( \frac{56}{12}\right)=1$$
$$p=5: x=5^0 \cdot 2 \cdot 7 \cdot 3^{-1} \mapsto 5^{-0}=1=\left |\frac{56}{12} \right |_5$$
$$w_5 \left ( \frac{56}{12}\right)=0$$
Could you tell me if it is right or if I have done something wrong? (Thinking)