Some congruences related to the q-Fermat quotients

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We give q-analogues of the following congruences by Z.-W. Sun: ∑ₖ₌₁ᵖ⁻¹Dₖ/k ≡ -2ᵖ⁻¹-1p p, ∑ₖ₌₁ᵖ⁻¹Hₖ/k 2ᵏ≡ 0 p, p 5, where p is a prime, Dₙ=∑ₖ₌₀ⁿn+k 2k2k k are the Delannoy numbers, and Hₙ=∑ₖ₌₁ⁿ1/k are the harmonic numbers. We also prove that, for any positive integer m and prime p>m+1, ∑1 k₁ kₘ p-11k₁ kₘ 2ᵏᵐ ≡1/2∑ₖ₌₁ᵖ⁻¹(-1)ᵏ⁻¹kᵐ p, which is a multiple generalization of Kohnen's congruence. Furthermore, a q-analogue of this congruence is established.