arXiv subjects
Publications and source records attributed to Zurab Aghdgomelashvili.
In the work is considered one of up to now unsolved by Hugo Steinhaus task on having integer length square and located in its plane point that are on integer distances from its vertexes.
Expressions of type $(p^q-1)/(p-1)$ and $a^2+ab+b^2$, where $a, b$ are natural and $p, q$ are prime numbers, are studied.
In this article one of the fundamental problems of Diophantine (integer) planar geometric figures, the Task max n(k), is considered.
The goal of the work is to take on and study one of the fundamental tasks studying Bidiophantine polygons (let us call a polygon Diophantine, if the distance between each two vertex of those is expressed by a natural number and we say that a Diophantine polygon is Bidiophantine if the coordinates of its each vertex are integer numbers).
The goal of the work is to take on and study one of the fundamental tasks studying Diophantine n-gons (the author of the paper considers an integral n-gon is Diophantine as far as determination of combinatorial properties of each of them requires solution of a certain Diophantine equation (equation sets)).