As of May 4 2007 the scripts will autodetect your timezone settings. Nothing here has to be changed, but there are a few things

## Wednesday, May 18, 2011

### Solving linear congruences ( NOT the M381 way )

In M381 Number Theory Unit 3 I read "...The way to become proficient at solving linear congruences is through plenty of practice at applying the above strategy. ..." - What did I just read?!

Well. This is NOT how it should be done. You need as much 'strategies' for solving linear congruences as you would need for solving a linear equality equation in x. There is a simple formula that solves -any- linear congruence equation.

a x ~ b mod m <=> x = Mod[a PowerMod[b, -1, m], m] where a, b can be ( negative ) fractions. ( Understanding the formula only requires understanding Greatest Common Divisors and the Euclidean Algorithm or one of its improved alternatives )

Example.
7 x ~ 41 mod 101 <=> x = Mod[41 PowerMod[7, -1, 101], 101] <=> x ~ 78 mod 101
Since:
7 * ( 78 + 101k ) - 41 = 505 + 707k which is clearly a multiple of 101 for any k.

#### 1 comment:

1. I found this information very helpful in solving the linear equations.The best method to solve these equations is graphical method.

## Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
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.)