MathDB

Find the minimum value of

k

such that there exists two sequence

{a_i},{b_i}

for

i=1,2,\cdots ,k

that satisfies the following conditions.
(i) For all

i=1,2,\cdots ,k,

a_i,b_i

is the element of

S=\{1996^n|n=0,1,2,\cdots\}.

(ii) For all

i=1,2,\cdots, k, a_i\ne b_i.

(iii) For all

i=1,2,\cdots, k, a_i\le a_{i+1}

and

b_i\le b_{i+1}.

(iv)

\sum_{i=1}^{k} a_i=\sum_{i=1}^{k} b_i.

Problem Statement