Problem B. 4650. (September 2014)

B. 4650. Is there a function of the form \(\displaystyle f(x)=\frac{ax+b}{cx+d}\) for which \(\displaystyle f(x_1)=x_2\), \(\displaystyle f(x_2)=x_3\), \(\displaystyle f(x_3)=x_4\), \(\displaystyle f(x_4)=x_5\), \(\displaystyle f(x_5)=x_1\) is true if \(\displaystyle x_1,\ldots,x_5\) are appropriate pairwise different real numbers?

Suggested by Gy. Károlyi, Budapest

(6 pont)

Deadline expired on October 10, 2014.

Statistics:

24 students sent a solution.
6 points:	Andó Angelika, Bereczki Zoltán, Csépai András, Fekete Panna, Geng Máté, Kovács 972 Márton, Nagy-György Pál, Porupsánszki István, Schefler Barna, Schwarcz Tamás, Szőke Tamás, Williams Kada.
0 point:	12 students.

Problems in Mathematics of KöMaL, September 2014