### Points on elliptic curves over finite fields

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For any partition of a set of squarefree numbers with relative density greater than 3/4 into two parts, at least one part contains three numbers whose product is a square. Also generalizations to partitions into more than two parts are discussed.

Solutions of the equations y² = xⁿ+k (n = 3,4) in a finite field are given almost explicitly in terms of k.

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