I believe to have proven something that I need for an algorithm I'm developing.

The proposition is:

Proof:

Substitution:

// see Greatest common divisor - Wikipedia, the free encyclopedia

Is this correct?

Thank you

Bernhard

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- February 26th 2010, 03:43 AMloopologylcm, gcd proof correct?
I believe to have proven something that I need for an algorithm I'm developing.

The proposition is:

Proof:

Substitution:

// see Greatest common divisor - Wikipedia, the free encyclopedia

Is this correct?

Thank you

Bernhard - February 26th 2010, 04:01 AMBacterius
Hello Bernhard,

Is the == sign a congruence ? ? If yes, what is the modulus considered ? Because a congruence without modulus is meaningless.

(Funny like we all get the same idea when we lack an congruence sign on the computer :D)

Out of curiosity, what is the algorithm you are developing about, if not too indiscrete ?

**EDIT**: ah, no, I get it, this is the conditional equivalence sign in the C language. Well obviously, if , then the equality holds, because , and . I don't really get your proof (what does it show ? a proof needs words), but I think you might get somewhere if you consider dividing the right hand side with the left hand side ... - February 26th 2010, 07:32 AMloopology
Hi Ray

Thanks for looking at my proof. Sorry for using a confusing notation (corrected it now).

I'm trying to prove that

holds, i.e. that can be calculated by

I believe to have proven the equivalence by applying what I hope are legal transformations to reach the equation

which is a valid connection between and (see Greatest common divisor - Wikipedia, the free encyclopedia) The cool thing about the substitution is that the equivalence applies for an arbitrary number of arguments to , i.e. which happens to be what I actually need, not just two arguments (i.e. ).

The algorithm is used for calculating BPMs to represent arbitrary rhythmic patterns. See Boss Dr.Beat DB-88