mersenneforum.org > Math residues and non residues of general quadratic congruences
 Register FAQ Search Today's Posts Mark Forums Read

 2012-10-12, 06:42 #1 smslca   Apr 2011 7 Posts residues and non residues of general quadratic congruences for a given range of x in Zn , and n is composite , and ax² + bx + c ≡ 0(mod n) and if (4a,n)=1, I learned that we can solve the congruence by (2ax + b)² ≡ b²-4ac (mod n) ==> y² ≡ z (mod n) but my question is , how many z values will be QR mod n and how many will be NQR and what about their distribution in Zn . And how many could be solved and how many could not be solved in the range of x values using y² ≡ z (mod n).? and can we predict x value for given z value , if x is some subset of Zn but not Zn I could only find literatures on n being a prime, but what if n is composite? For example , let n = 38411 and 100 So , can any one suggest , where can i find literature on my doubt . or even books or any means i can solve my problem. can anyone guide me in wright and exact path , i should take. If i am wrong or obscure any where in my question , hope will be notified to me.

 Similar Threads Thread Thread Starter Forum Replies Last Post LaurV Math 18 2017-09-16 14:47 zippy Math 6 2015-07-20 13:09 NBtarheel_33 Data 19 2015-04-21 16:02 Romulas Math 3 2010-05-09 03:27 jinydu Lounge 1 2008-09-16 17:02

All times are UTC. The time now is 11:17.

Mon Dec 6 11:17:36 UTC 2021 up 136 days, 5:46, 0 users, load averages: 1.70, 1.97, 3.02