Jorma K. Merikoski

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We present an asymptotic formula for the number of line segments connecting q + 1 points of an n × n square grid, and a sharper formula, assuming the Riemann hypothesis. We also present asymptotic formulas for the number of lines through at least q points and, respectively, through exactly q points of the grid. The well-known case q = 2 is so generalized.
We give a set of axioms to establish a perpendicularity relation in an Abelian group and then study the existence of perpendicularities in (Z í µí±› , +) and (Q + , ⋅) and in certain other groups. Our approach provides a justification for the use of the symbol ⊥ denoting relative primeness in number theory and extends the domain of this convention to some(More)
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