I am stuck on the following question in Lam's quadratic forms for a few days now. Let $a,b,c$ be three elements of a field $F$ such that $0 \neq a^2+b^2 \neq c^2$. Show that the quadratic form $\langle a^2+b^2, a^2 +b^2 - c^2 \rangle$ represents 1. In general, how does one determine if a quadratic form determines 1 or not?
2026-04-02 13:30:32.1775136632
Does this quadratic form represent 1?
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