### On some Applications of Graph Theory to Number Theoretic Problems

Heilbronn Number Theory Seminar

21st March 2018, 4:00 pm – 5:00 pm

Howard House, 4th Floor Seminar Room

How large can a set of integers be, if the equation a_1a_2...a_h=b_1b_2...b_h has no solution consisting of distinct elements of this set? How large can a set of integers be, if none of them divides the product of h others? How small can a multiplicative basis for {1, 2, ..., n} be? The first question is about a generalization of the multiplicative Sidon-sets, the second one is of the primitive sets, while the third one is the multiplicative version of the well-studied analogue problem for additive bases.

In answering the above mentioned questions graph theory plays an important role and in most of our results not only the asymptotics are found, but very tight bounds are obtained for the error terms, as well. This is joint work with Csaba Sándor.

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