Talk:Quadratic residuosity problem

Spelling
Residuacity is definitely correct. It is mathematical terminology, and more than a century old. Charles Matthews 11:00, 22 February 2006 (UTC)


 * The phrase "quadratic residuacity" returns 81 hits on Google, whereas "quadratic residuosity" returns 16,500 hits. The overwhelmingly commonly used term is "residuosity", not "residuacity". Also, every textbook I've seen uses the "residuosity" spelling. &mdash;Lowellian (reply) 04:34, 25 May 2006 (UTC)

Doesn't make it good English, it means people copy each other. Residual is correct while *residuous doesn't even exist. So residuosity is mal-formed (viscous &rarr; viscosity, yes, but here the adjective isn't there). Charles Matthews 09:46, 25 May 2006 (UTC)

The word residuous does exist, check any dictionary. 217.34.253.153 (talk) 14:28, 11 April 2011 (UTC)

Too specific as presented?
The article refers to $$N=pq$$ with $$p, q$$ unknown. Doesn't this however apply to all $$N$$ where at least one prime factor is unknown (and it is not known to have even multiplicity)? Since perfect powers are easily detected using Householder's method, this effectively means that at least two prime factors are unknown.

Of course, $$N=pq$$ is the one that is most important e.g. in cryptography, I'm just pointing out that it should not be assumed that e.g. $$N=pqr$$ with three unknown primes, or $$N=pq^2$$ were solved problems. (If $$N$$ is a perfect power, the problem can be reduced to deciding it for $$N$$'s least integer root, though, by applying one of Householder's methods.) Aragorn2 (talk) 12:07, 16 April 2019 (UTC)