5

Part of 1993 Taiwan National Olympiad

Problems(1)

$A=\{a_1,a_2,...,a_{12}\}

Source: 2-nd Taiwanese Mathematical Olympiad 1993

A=\{a_{1},a_{2},...,a_{12}\}

is a set of positive integers such that for each positive integer

n \leq 2500

there is a subset

S

A

whose sum of elements is

n

a_{1}<a_{2}<...<a_{12}

, what is the smallest possible value of

a_{1}

number theory unsolvednumber theory