MathDB

1

Part of 2014 Dutch IMO TST

Problems(2)

Determine all paris (a,b)

Source: Dutch IMO TST I Problem 1

7/17/2014
Determine all pairs (a,b)(a,b) of positive integers satisfying a^2+b\mid a^2b+a \text{and}  b^2-a\mid ab^2+b.
number theory proposednumber theory
Function with prime divisors

Source: Dutch IMO TST II Problem 1

7/17/2014
Let f:Z>0→R f:\mathbb{Z}_{>0}\rightarrow\mathbb{R} be a function such that for all n>1n > 1 there is a prime divisor pp of nn such that f(n)=f(np)−f(p). f(n)=f\left(\frac{n}{p}\right)-f(p). Furthermore, it is given that f(22014)+f(32015)+f(52016)=2013 f(2^{2014})+f(3^{2015})+f(5^{2016})=2013 . Determine f(20142)+f(20153)+f(20165) f(2014^2)+f(2015^3)+f(2016^5) .
functionalgebra unsolvedalgebra