Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1997. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 24)

PHONG, B. M., A characterization of the identity function

6 Bui Minh Phong On the other hand, it follows from (4) that /(11) - /(

3

2 + 2) = /(10) + D = /(2)/(5) + D = /(

2)

2 + /(2)/(3) + /(3) - /(2), which, together with the last relation, implies (12) /(2)

2 = 2/(2), and /(13) = /(

l

2 + 3

2 + 3) = /(2) + /(11) = 2/(2) + /(2)/(3) + /(3). Finally, the relation (10) together with the fact /(8) = /(

l

2 + 2

2 + 3) = /(2) + /(6) - /(5) + /(3) show that (13) /(2)/(3) = 2/(3). Moreover (14) = /(

5

2 + 1) = /(26) = /(2)/(13) = 4/(2) + 6/(3), = /(6

2 + 1) - /(37) - /(3

2 + 5

2 + 3) 1 j =/(11)+ /(26) = 5/(2)+ 9/(3), (16) 2/(17) = /(4

2 + 4

2 + 3) - = /(35)-£ = /(5)/(7) - 2?, and (17) /(3)/(7) = /(21) = /(3

2 + 3

2 + 3) = 2/(10) + D = 3/(2) + 5/(3). The equation (12) shows that either /(2) = 0 or /(2) = 2. Assume that /(2) = 0. Then (13) implies that /(3) = 0 and so, by using (10)-(17) we have S\ = S2 = S3 = S4 = = Sß = 0, from which follows that (2) is true.