Given an integer d ≥ 2, what is the smallest r so that there is a set of binary quadratic formsg (f1,...,fr) for which (fdj) is nontrivially linearly dependent? We show that ifr ≤4, then d ≤5, and for d ≥ 4, construct such a set with r =d/2+2. Many explicit examples are given, along with techniques for producing others.
- Polynomial identities
- Super-Fermat problem for forms
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