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smslca
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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.
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.
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