A Somos k sequence is a sequence defined by a bilinear recurrence relation of order k. For example, an elliptic divisibility sequence, which consists of the values of the division polynomials of an elliptic curve, is a Somos 4 sequence. It is known that Somos 4 sequences are periodic modulo all but finitely many primes. In this talk, we discuss periodicity of Somos sequences modulo primes when the sequences are related to curves of genus 2. In particular, we show that the Somos 8 sequence which consists of the values of Cantor’s division polynomials of a curve of genus 2 is periodic modulo all but finitely many primes. This talk is based on joint work with Yasuhiro Ishitsuka, Tetsushi Ito, Tatsuya Ohshita, and Takashi Taniguchi.

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