Multiples of 32

What is the smallest possible positive integer value of β,\beta, such that for some integers α,\alpha, γ,\gamma, δ,\delta, and ϵ \epsilon , the following condition is true?

Condition: For every five-digit number abcde \overline{abcde} that is a multiple of 32,32, αa+βb+γc+δd+ϵe \alpha a + \beta b + \gamma c + \delta d + \epsilon e is also a multiple of 32.32.

Details and assumptions

abc \overline{abc} means 100a+10b+1c 100a + 10b + 1c, as opposed to a×b×c a \times b \times c. As an explicit example, for a=2,b=3,c=4a=2, b=3, c=4, abc=234\overline{abc} = 234 and not 2×3×4=24 2 \times 3 \times 4 = 24.

×

Problem Loading...

Note Loading...

Set Loading...