Sur un système linéaire de Terjanian
In 1989, Terjanian tried to prove the first case of Fermat’s Last Theorem for any odd prime exponent $l$ using cyclotomic units and Hilbert symbols. His proof was incomplete since it relied on a conjecture, named $LC$. He also defined a property $P$ that implies $LC$ and that is phrased simply using linear equations over the finite field with $l$ elements. We prove that this property $P$ is false for almost all prime numbers $l$, and in particular when $l-1$ has a prime factor greater than or equal to $11$.