A simple polynomial for a simple transposition

Details A simple polynomial for a simple transposition A simple polynomial for a simple transposition

2006-03-02

arxiv.org/abs/math/0603054v1

Mathematics

Number Theory

4 pages

Scientific paper

In this note, we review some facts about polynomials representing functions
modulo primes p. In addition we prove that the polynomial f(x) = x^{p-2} +
x^{p-3} + ... + x^3 + x^2 + 2x + 1 represents the transposition (0 1) modulo p,
that is, f(0) \equiv 1 (mod p), f(1) \equiv 0 (mod p), and f(a) \equiv a (mod
p) for all 2 \le a \le p-1.

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