MathDB

For a sequence

a_1,a_2,...,a_m

of real numbers, define the following sets

A=\{a_i | 1\leq i\leq m\}\ \text{and} \ B=\{a_i+2a_j | 1\leq i,j\leq m, i\neq j\}

Let

n

be a given integer, and

n>2

. For any strictly increasing arithmetic sequence of positive integers, determine, with proof, the minimum number of elements of set

A\triangle B

, where

A\triangle B

= \left(A\cup B\right) \setminus \left(A\cap B\right).

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