For primes p>q, all skew braces of order pq are explicitly constructed: only the trivial brace if p is not 1 modulo q, and exactly 2q+2 braces if p is 1 modulo q.
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Skew braces of size $pq$
For primes p>q, all skew braces of order pq are explicitly constructed: only the trivial brace if p is not 1 modulo q, and exactly 2q+2 braces if p is 1 modulo q.