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On R. Chapman's "evil determinant": case p ≡ 1 (mod 4)

Maxim Vsemirnov — 2013

Acta Arithmetica

For p ≡ 1 (mod 4), we prove the formula (conjectured by R. Chapman) for the determinant of the (p+1)/2 × (p+1)/2 matrix $C = (C_{i j})$ with $C_{i j} = ((j - i) / p)$ .

The group Sp10(ℤ) is (2,3)-generated

Vadim Vasilyev; Maxim Vsemirnov — 2011

Open Mathematics

It is proved that the group Sp10(ℤ) is generated by an involution and an element of order 3.

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