Hou and Liu developed a telescoping method to prove the congruence of partial sums of P-recursive sequences. We release the requirement on the telescoper and utilize the congruence of the sequence. With this approach, we are able to confirm a conjecture of Sun and find a new congruence on the central trinomial coefficient.
A congruence involving products of $q$-binomial coefficients
Partial sums of the Gibonacci sequence
Partial sums and generating functions of products of Horadam numbers with indices in arithmetic progression
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