We give a representation of any integer as a vector of the Witt ring W(Z_p) and relate it to the Fermat quotient q(n) = (n^(p−1) − 1)/p. Logarithms are introduced in order to establish an isomorphism between the commutative unipotent groups 1+ pW(Z_p) and W(Z_p).
DI BARTOLO A, FALCONE G (2008). Witt vectors and Fermat quotient. JOURNAL OF NUMBER THEORY, 128, 1376-1387 [10.1016/j.jnt.2007.11.003].
Witt vectors and Fermat quotient
DI BARTOLO, Alfonso;FALCONE, Giovanni
2008-01-01
Abstract
We give a representation of any integer as a vector of the Witt ring W(Z_p) and relate it to the Fermat quotient q(n) = (n^(p−1) − 1)/p. Logarithms are introduced in order to establish an isomorphism between the commutative unipotent groups 1+ pW(Z_p) and W(Z_p).
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