Exercise · ZW-LEGENDRE-SYMBOL-008 · ★★☆ Intermediate
Compute \(\left(\frac{2}{p}\right)\) for \(p=17\) using that \(6^2\equiv 2\pmod{17}\).
Choose one option.
Show answer
- A. \(1\)
Explanation
Since \(2\) is the square of \(6\) modulo 17, the symbol equals 1 by the definition of a quadratic residue.
Review the concept: Legendre symbol
The Legendre symbol \(\left(\frac{a}{p}\right)\) for an odd prime \(p\) and an integer \(a\) with \(p \nmid a\) equals \(1\) if \(a\) is a quadratic residue modulo \(p\), and \(-1\) if it is not.
\[\left(\frac{a}{p}\right)\equiv a^{(p-1)/2} \pmod{p}\]
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