## The least common multiple and lattice points on hyperbolas.(English)Zbl 0983.11058

Let $$a_1a_2,\dots, a_k$$ be $$k$$ given integers with $$X\leq a_1< a_2<\dots< a_k\leq X+L$$. The main result of the paper is an estimation for the lower bound of the least common multiple $$\text{LCM} [a_1,a_2,\dots, a_k]$$. From this, one can derive an estimation for the number of lattice points on a short arc of a hyperbola. Assume that $$k$$ distinct lattice points $$(a_i,b_i)$$ are lying on the hyperbola $$ab=N$$ with $$a_1< a_2<\dots< a_k$$. Then a lower bound for $$a_k-a_1$$ is given.

### MSC:

 11P21 Lattice points in specified regions
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