2

Part of 2008 Swedish Mathematical Competition

Problems(1)

2 number from 1-n such that their product = sum of other n-2

Source: 2008 Swedish Mathematical Competition p2

Determine the smallest integer

n \ge 3

with the property that you can choose two of the numbers

1,2,\dots, n

in such a way that their product is equal to the sum of the other

n - 2

languages. What are the two numbers?

number theorycombinatorics