It is a classical unsolved problem whether there is a polynomial with integral coef- ficients whose values at natural numbers form a Sidon set. In this note we prove the existence of a polynomial of degree 5, with real coeficients, such that the integer parts of the values form a Sidon set.
Concluding remark It would be interesting to know whether it is possible to generalize the method of the previous section to all commutative locally compact groups. For a long time I tried in vain to do this. Mauclaire uses a different approach. He applies the structure theory of locally compact groups to reduce the general case to certain subcases, which were studied in this paper.