3

Part of 2002 Irish Math Olympiad

Problems(2)

Source: Ireland 2002

Find all triples of positive integers

(p,q,n)

p

q

primes, satisfying: p(p\plus{}3)\plus{}q(q\plus{}3)\equal{}n(n\plus{}3).

number theory unsolvednumber theory

find all functions

Source: Ireland 2002

Find all functions

f: \mathbb{Q} \rightarrow \mathbb{Q}

such that: f(x\plus{}f(y))\equal{}y\plus{}f(x) for all

x,y \in \mathbb{Q}

functionalgebrafunctional equationalgebra unsolved