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Residues and non residues of general quadratic congruences

  1. Oct 12, 2012 #1
    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)

    So, if n is composite,

    Sometimes I see, modulo 4an, when do we take 4an and n ,

    how can we prove , there exists residues and non-residues as z values. for any range of x in Zn
    Is there any range of x in general , such that there exists only either residues or non residues as solutions.

    If i am wrong or obscure any where in my question , hope will be notified to me.
     
    Last edited: Oct 12, 2012
  2. jcsd
  3. Oct 12, 2012 #2
    sorry i messed it up, please help me to delete the post
     
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