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Saturday, October 22, 2011

Solving quadratic congruence equations in Mathematica

This is as yet the last post in the LQR series. If you are only interested in -solving- ( quadratic ) congruence equations then this is the way to do it in Mathematica:

As a general Diophantic equation:
In[1]:= Reduce[x^2==123456+1299709 k,{x,k},Integers] Out[1]= (C[1]\[Element]Integers&&x==427784-1299709 C[1]&&k==140800-855568 C[1]+1299709 C[1]^2)||(C[1]\[Element]Integers&&x==871925-1299709 C[1]&&k==584941-1743850 C[1]+1299709 C[1]^2)

Or slightly more elegant as a pure congruence equation ( thanks to: Mr. Wizard ):
In[2]:= Reduce[x^2 == 123456, x, Modulus -> 1299709] Out[2]= x == 427784 || x == 871925

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Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
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To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)