Let q be a prime. We classify the odd primes p ≠ q such that the equation x2 ≡ q (mod p) has a solution, concretely, we find a subgroup L4q of the multiplicative group U4q of integers relatively prime with 4q (modulo 4q) such that x2 ≡ q (mod p) has a solution iff p ≡ c (mod 4q) for some c ∈ L4q. Moreover, L4q is the only subgroup of U4q of half order containing −1.
Dergi Türü : Uluslararası
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