MathDB

1

Part of 1987 IberoAmerican

Problems(2)

Find the function [IberoAmerican 1987]

Source:

11/12/2010
Find the function f(x)f(x) such that f(x)2f(1−xx+1)=64xf(x)^2f\left(\frac{1-x}{x+1}\right) =64x for x≠0,x≠1,x≠−1x\not=0,x\not=1,x\not=-1.
functionalgebra proposedalgebra
Iberoamerican 1987.5

Source: IberoAmerican 1987 Q4

10/27/2006
The sequence (pn)(p_n) is defined as follows: p1=2p_1=2 and for all nn greater than or equal to 22, pnp_n is the largest prime divisor of the expression p1p2p3…pn−1+1p_1p_2p_3\ldots p_{n-1}+1. Prove that every pnp_n is different from 55.
number theoryalgebra proposedalgebra