What is the smallest possible positive integer value of β, such that for some integers α, γ, δ, and ϵ, the following condition is true?
Condition: For every five-digit number abcde that is a multiple of 32, αa+βb+γc+δd+ϵe is also a multiple of 32.
Details and assumptions
abc means 100a+10b+1c, as opposed to a×b×c. As an explicit example, for a=2,b=3,c=4, abc=234 and not 2×3×4=24.