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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.10881 |
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Table of Contents:
- We expand the class of linear symmetric equations for which large sets with no non-trivial solutions are known. Our idea is based on first finding a small set with no solutions and then enlarging it to arbitrary size using a multi-dimensional construction, crucially assuming the equation in primitive. We start by presenting the technique on some new equations. Then we use it to show that a symmetric equation with randomly chosen coefficients has a near-optimal set with no non-trivial solutions. We also show a construction for a wide class of symmetric equation in 6 variables. In the final section we present a couple of remarks on non-symmetric equations.