# Problem 122: Efficient exponentiation
The most naive way of computing n15 requires fourteen multiplications: n
× n × ... × n = n15 But using a "binary" method you can compute it in
six multiplications: n × n = n2n2 × n2 = n4n4 × n4 = n8n8 × n4 = n12n12
× n2 = n14n14 × n = n15 However it is yet possible to compute it in only
five multiplications: n × n = n2n2 × n = n3n3 × n3 = n6n6 × n6 = n12n12
× n3 = n15 We shall define m(k) to be the minimum number of
multiplications to compute nk; for example m(15) = 5. For 1 ≤ k ≤ 200,
find ∑ m(k).