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The circulant Hadamard matrix conjecture, first stated in print by Ryser in 1963. It can be stated as follows. If $n>4$, then there does not exist a sequence $(a_1,a_2,\dots,a_n)$ of $\pm 1$'s satisfying $$\sum_{i=1}^n a_i a_{i+k}=0,\ 1\leq k\leq n-1,$$ where the subscript $i+k$ is taken modulo $n$.