Re: "badmod" solving equations in modular arithmetic
- To: mathgroup at smc.vnet.net
- Subject: [mg37796] Re: [mg37761] "badmod" solving equations in modular arithmetic
- From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
- Date: Wed, 13 Nov 2002 01:11:20 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Yes, unfortunately there is a limitation on the size of Modulus in such functions. However, for this sort of equation you can find a solution as follows: In[1]:= <<NumberTheory`NumberTheoryFunctions` In[2]:= SqrtMod[SqrtMod[-14436,457381],457381] Out[2]= 368466 Checking: In[3]:= PowerMod[%,4,457381]==Mod[-14436,457381] Out[3]= True Andrzej Kozlowski Yokohama, Japan http://www.mimuw.edu.pl/~akoz/ http://platon.c.u-tokyo.ac.jp/andrzej/ On Tuesday, November 12, 2002, at 05:13 PM, AGUIRRE ESTIBALEZ Julian wrote: > Dear MathGroup, > > I need to solve equations in modular arithmetic with large prime > modulus. One example is > > Solve[{x^4 == -14436, Modulus == 457381}] > > for which I get the message > > Roots::badmod: Cannot extract roots of input modulo 457381 > > Is there a known limit on the size of Modulus? In fact, I do not need > the > solutions, I just need to know if there are any. So my second > question: is > there a bulit-in function or a package that computes a "cuartic" > JacobiSymbol? > > Thanks, > > Julian Aguirre | Voice: +34 946012659 > Departamento de Matematicas | Fax: +34 944648500 > Universidad del Pais Vasco | Postal: Aptdo. 644, 48080 Bilbao, Spain > | email: mtpagesj at lg.ehu.es > > > >