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-   -   A useful function. (https://www.mersenneforum.org/showthread.php?t=23094)

 JM Montolio A 2018-02-26 11:26

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
Spain

 Nick 2018-02-26 14:22

[QUOTE=JM Montolio A;480917]for (m,n ) coprimes, M(n*m)= (M(n)*M(m))/(mcd(M(n),M(m))
[/QUOTE]
What is the mcd function that you are using?

 Dr Sardonicus 2018-02-26 14:53

[QUOTE=JM Montolio A;480917]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)[/QUOTE]

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)?

 JM Montolio A 2018-02-26 17:00

yes , gcd . En Español "El Máximo".

[QUOTE=Nick;480930]What is the mcd function that you are using?[/QUOTE]

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

 JM Montolio A 2018-02-26 17:05

M( only for odd integer number)

M() Only for odd numbers.

 JM Montolio A 2018-02-26 17:08

and more: properties

d | n, then M(d) | M(n).

 science_man_88 2018-02-26 17:15

[QUOTE=JM Montolio A;480949]Yes, gcd(). En español "El máximo".
JM M[/QUOTE]

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.

 JM Montolio A 2018-02-26 17:36

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

[SIZE=1]

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

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

JM M[/SIZE]
[SIZE=1]
[/SIZE]

 CRGreathouse 2018-02-26 17:55

[QUOTE=JM Montolio A;480917]¿ useful function ?[/QUOTE]

How do you compute it?

 JM Montolio A 2018-02-26 18:03

well, is only one axiomatic definition.

 JM Montolio A 2018-02-26 18:06

other propertie M( 2^e - 1 ) = e.

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

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