Abstract
We present simple congruences modulo [Formula: see text] of the Jones polynomial for the torus link [Formula: see text], where [Formula: see text] is a prime number and [Formula: see text] is a nonzero integer. These congruences are expressed in terms of Chebyshev polynomials and quantum numbers. The approach makes elementary use of the Kauffman bracket and does not require any representation theory.
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