Three families of q-supercongruences modulo the square
and cube of a cyclotomic polynomial
In this paper, three parametric q-supercongruences for truncated
very-well-poised basic hypergeometric series are proved,
one of them modulo the square, the other two modulo the cube
of a cyclotomic polynomial. The main ingredients of proof include
a basic hypergeometric summation by George Gasper, the method of
creative microscoping (a method recently introduced by the first author
in collaboration with Wadim Zudilin),
and the Chinese remainder theorem for coprime polynomials.
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