Topology of Numbers · Problem 6.3.5

Representations by Quadratic Forms — Allen Hatcher

Mathematics — Number Theory · principal-form-characters

Problem

Show that for a positive nonsquare discriminant Δ\Delta, if the principal form represents −1-1 then all odd primes pp dividing Δ\Delta must satisfy p≡1(mod4)p \equiv 1 \pmod{4}. Hint: Use χp\chi_p.

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