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Old 2018-02-26, 11:26   #1
JM Montolio A
 
Feb 2018

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Smile A useful function.

Hi,


Define M(n) as:


for (p^e), M( p^e ) = M(p)*(p ^ (e-1) )


for (m,n ) coprimes, M(n*m)= (M(n)*M(m))/(mcd(M(n),M(m))


for p prime, p | (2^M(p)-1)


¿ useful function ?


JM M
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Old 2018-02-26, 14:22   #2
Nick
 
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Quote:
Originally Posted by JM Montolio A View Post
for (m,n ) coprimes, M(n*m)= (M(n)*M(m))/(mcd(M(n),M(m))
What is the mcd function that you are using?
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Old 2018-02-26, 14:53   #3
Dr Sardonicus
 
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Quote:
Originally Posted by JM Montolio A View Post
Hi,


Define M(n) as:


for (p^e), M( p^e ) = M(p)*(p ^ (e-1) )

for (m,n ) coprimes, M(n*m)= (M(n)*M(m))/(mcd(M(n),M(m))

for p prime, p | (2^M(p)-1)
I object, on the following grounds:

(1) The requirement p | (2^M(p)-1) is not a definition. Assuming M(p) takes positive integer values, M(2) is problematic. The only possible integer value of M(2) is zero. For odd p, M(p) merely has to be divisible by the multiplicative order of 2 (mod p).

(2) The expression (mcd(M(n),M(m)) has an extra left parenthesis.

(3) The function mcd() is undefined. Do you perhaps mean gcd() (greatest common divisor)?
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Old 2018-02-26, 17:00   #4
JM Montolio A
 
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Red face yes , gcd . En Español "El Máximo".

Quote:
Originally Posted by Nick View Post
What is the mcd function that you are using?




Yes, gcd(). En español "El máximo".
JM M

Last fiddled with by JM Montolio A on 2018-02-26 at 17:01
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Old 2018-02-26, 17:05   #5
JM Montolio A
 
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Red face M( only for odd integer number)

M() Only for odd numbers.
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Old 2018-02-26, 17:08   #6
JM Montolio A
 
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Smile and more: properties

d | n, then M(d) | M(n).
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Old 2018-02-26, 17:15   #7
science_man_88
 
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Quote:
Originally Posted by JM Montolio A View Post
Yes, gcd(). En español "El máximo".
JM M
Think the reason m isn't used in english is it could be maximal or minimal. Also without a definition at the primes I'm not sure the definition is complete M(p)=M(p)*1 is not all that helpful.

Last fiddled with by science_man_88 on 2018-02-26 at 17:20
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Old 2018-02-26, 17:36   #8
JM Montolio A
 
Feb 2018

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Cool well, for p prime, M(p) must be the correct value.





- N*D = 2^M(n) -1


- for p prime , M(p)|(p-1)

JM M



Last fiddled with by JM Montolio A on 2018-02-26 at 17:37
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Old 2018-02-26, 17:55   #9
CRGreathouse
 
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Quote:
Originally Posted by JM Montolio A View Post
¿ useful function ?
How do you compute it?
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Old 2018-02-26, 18:03   #10
JM Montolio A
 
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well, is only one axiomatic definition.
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Old 2018-02-26, 18:06   #11
JM Montolio A
 
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Red face other propertie M( 2^e - 1 ) = e.

other property, M( 2^e - 1 ) = e.
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