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Find the solution of x^2≡7 mod 19(a) x≡±16 mod 23(b) x≡±11 mod 23(c) x≡±14 mod 23(d) x≡±7 mod 23This question was posed to me in semester exam.This interesting question is from Number Theory topic in division More Number Theory of Cryptograph & Network Security

Answer»

Correct ANSWER is (b) x≡±11 mod 23

To elaborate: a=77^((19+1)/4)≡7^5≡1(QR and there is solution)

x ≡ ±7(19 + 1)/4 (mod 19) ≡±11i.e. x = 11 and 12.



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