4

Part of 2012 Bosnia Herzegovina Team Selection Test

Problems(1)

Bosnia and Herzegovina TST 2012 Problem 4

Source:

Define a function

f:\mathbb{N}\rightarrow\mathbb{N}

f(1)=p+1,

f(n+1)=f(1)\cdot f(2)\cdots f(n)+p,

p

is a prime number. Find all

p

such that there exists a natural number

k

f(k)

is a perfect square.

functioninductionalgebrapolynomialmodular arithmeticnumber theory proposednumber theory