I'm working on modernizing Rosetta Code's infrastructure. Starting with communications. Please accept this time-limited open invite to RC's Slack.. --Michael Mol (talk) 20:59, 30 May 2020 (UTC)

Talk:Jacobi symbol

From Rosetta Code

Promote to Task[edit]

This task is well defined and has many implementation. Any objection to promoting this draft task to a task?

--DavidFashion (talk) 22:55, 5 February 2020 (UTC)

Lead rewrite[edit]

I rewrote the lead to use LaTeX, but Mathoid wasn't working when I tried to preview it, so I'm dumping it here so that I don't lose it. Disregard the errors if it doesn't re-render by the time you see this. -happy5214 06:22, 6 February 2020 (UTC)


The Jacobi symbol is a multiplicative function that generalizes the Legendre symbol. Specifically, the Jacobi symbol Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("<p>There was a problem during the HTTP request: 503 Service Unavailable </p>") from server "http://mathoid.testme.wmflabs.org":): \left(\frac{a}{n}\right)

equals the product of the Legendre symbols Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("<p>There was a problem during the HTTP request: 503 Service Unavailable

</p>") from server "http://mathoid.testme.wmflabs.org":): \left(\frac{a}{p_i}\right)^{k_i} , where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("<p>There was a problem during the HTTP request: 503 Service Unavailable </p>") from server "http://mathoid.testme.wmflabs.org":): n = p_1^{k_1}p_2^{k_2}\cdots p_i^{k_i}

is the prime factorization of  and the Legendre symbol Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("<p>There was a problem during the HTTP request: 503 Service Unavailable

</p>") from server "http://mathoid.testme.wmflabs.org":): \left(\frac{a}{p}\right)

denotes the value of  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("<p>There was a problem during the HTTP request: 503 Service Unavailable

</p>") from server "http://mathoid.testme.wmflabs.org":): a^{(p-1)/2} \pmod{p} = \begin{cases} 1 & \text{if a is a square} \pmod{p} \\ -1 & \text{if a is not a square} \pmod{p} \\ 0 & \text{if } a \equiv 0 \pmod{p} \end{cases}


If n is prime, then the Jacobi symbol Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("<p>There was a problem during the HTTP request: 503 Service Unavailable </p>") from server "http://mathoid.testme.wmflabs.org":): \left(\frac{a}{n}\right)

equals the Legendre symbol Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("<p>There was a problem during the HTTP request: 503 Service Unavailable

</p>") from server "http://mathoid.testme.wmflabs.org":): \left(\frac{a}{n}\right) .

Task

Calculate the Jacobi symbol Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("<p>There was a problem during the HTTP request: 503 Service Unavailable </p>") from server "http://mathoid.testme.wmflabs.org":): \left(\frac{a}{n}\right) .