can anyone solve this?

[pokerowned]

Being a some constant, further assume that we
are in a factor ring (basically all operations modulo some sumber p). Note, that the division below is a multiplication by the modular inverse.
You always have to start with x=9.
Consider the following recursive formula:

new_x = (x²-1)² / (4*x*(x²+a*x+1))


How often do you have to perform this operation to get a specific x (basically getting the new_x and feeding it back into the formula to get another new_x, and so on)?
Note: You can start multiple such chains beginning at x=9, and add the resulting x values
using the addition algorithm from http://en.wikipedia.org/wiki/Montgomery_curve (Montgomery arithmetic section).
Note, that the x value, is the value you get at the end of such calculation-chain, and the z value is always 1.

 

[Deleted member 4993]

Being a some constant, further assume that we
are in a factor ring (basically all operations modulo some sumber p). Note, that the division below is a multiplication by the modular inverse.
You always have to start with x=9.
Consider the following recursive formula:

new_x = (x²-1)² / (4*x*(x²+a*x+1))


How often do you have to perform this operation to get a specific x (basically getting the new_x and feeding it back into the formula to get another new_x, and so on)?
Note: You can start multiple such chains beginning at x=9, and add the resulting x values
using the addition algorithm from http://en.wikipedia.org/wiki/Montgomery_curve (Montgomery arithmetic section).
Note, that the x value, is the value you get at the end of such calculation-chain, and the z value is always 1.

What are your thoughts?

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[HallsofIvy]

In general, "arithmetic modulo p" is a ring (so division is defined) only if p is prime. Is that what you intended? And it looks to me like the answer to your question will depend upon both x and p, Do you want a general answer or do you have a specific p in mind?

 

[pokerowned]

guys im not a math student nor am i required to do this problem. someone posted this problem in another place and i wanted to post the answer just for bragging rights. im in no waygianing from this. if someone can answer it cool, if not thats cool also. not a big deal

 

[Ishuda]

Cool. Bye.

Hey Halls, go have a look here (too much!):
https://bitcointalk.org/index.php?topic=939215.new

Looks like this guy was trying for a "bounty" promised to whoever solved this :cool:

Actually I believe with the way it is stated, that the answer is "there is no solution". That is consider p=2, i.e. the binary numbers 0 and 1. 1 has a multiplicative inverse of 1 and 0 has no multiplicative inverse. 4 x is congruent to zero mod 2, so the second number in the sequence does not produce a number and you must stop because you have no new_x. Or to put it another way, 'Starting at 9 mod 2, you can't use the given recursion formula to get zero no matter the value of a'.