MathDB

6

Part of 2004 South africa National Olympiad

Problems(1)

These three integers cannot all be prime

Source: South African MO 2004 Q6

5/27/2012
The numbers a1,a2a_1,a_2 and a3a_3 are distinct positive integers, such that
(i) a1a_1 is a divisor of a2+a3+a2a3a_2+a_3+a_2a_3;
(ii) a2a_2 is a divisor of a3+a1+a3a1a_3+a_1+a_3a_1;
(iii) a3a_3 is a divisor of a1+a2+a1a2a_1+a_2+a_1a_2.
Prove that a1,a2a_1,a_2 and a3a_3 cannot all be prime.
inductionnumber theory unsolvednumber theory