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 18:16.

Sun Jul 3 18:16:10 UTC 2022 up 80 days, 16:17, 0 users, load averages: 1.81, 1.72, 1.60

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.

≠ ± ∓ ÷ × · − √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °
∠ ∟ ° ≅ ~ ‖ ⟂ ⫛
≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘ ∏ ∐ ∑ ∧ ∨ ∩ ∪ ⨀ ⊕ ⊗ 𝖕 𝖖 𝖗 ⊲ ⊳
∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟
¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣ … ⋯ ⋮ ⋰ ⋱
∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ
𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎𝜍 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔