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Math Help - residues and non residues of general quadratic congruences

  1. #1
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    residues and non residues of general quadratic congruences

    for a given range of x in Zn , and n is composite , and ax + bx + c ≡ 0(mod n) and if (4a,n)=1,
    I learned that we can solve the congruence by (2ax + b) ≡ b-4ac (mod n) ==> y ≡ 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 taken from 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 by ssnmanikanta; October 12th 2012 at 01:42 AM.
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  2. #2
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    Re: residues and non residues of general quadratic congruences

    sorry i messed it up, please help me to delete the post
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