MathDB

2

Part of 2002 Irish Math Olympiad

Problems(2)

acquaintances

Source: Ireland 2002

7/5/2009
(a) (a) A group of people attends a party. Each person has at most three acquaintances in the group, and if two people do not know each other, then they have a common acquaintance in the group. What is the maximum possible number of people present? (b) (b) If, in addition, the group contains three mutual acquaintances, what is the maximum possible number of people?
combinatorics proposedcombinatorics
determine n

Source: Ireland 2002

7/5/2009
Suppose n n is a product of four distinct primes a,b,c,d a,b,c,d such that: (i) (i) a\plus{}c\equal{}d; (ii) (ii) a(a\plus{}b\plus{}c\plus{}d)\equal{}c(d\minus{}b); (iii) (iii) 1\plus{}bc\plus{}d\equal{}bd. Determine n n.
number theory proposednumber theory