2

Part of 2004 Pan African

Problems(2)

Is it an integer?

Source: Pan African 2004

4\sqrt{4-2\sqrt{3}}+\sqrt{97-56\sqrt{3}}

special factorizations

Source: Pan African 2004

Each of the digits

1

3

7

9

occurs at least once in the decimal representation of some positive integers. Prove that one can permute the digits of this integer such that the resulting integer is divisible by

7