Let a0,a1,…,a2024 be real numbers such that ∣ai+1−ai∣≤1 for i=0,1,…,2023.
a) Find the minimum possible value of a0a1+a1a2+⋯+a2023a2024
b) Does there exist a real number C such that a0a1−a1a2+a2a3−a3a4+⋯+a2022a2023−a2023a2024≥C for all real numbers a0,a1,…,a2024 such that ∣ai+1−ai∣≤1 for i=0,1,…,2023.