1 citations · 4 across the 36 of their papers we have counts for
36 papers
The sum of the squares of p positive integers which are consecutive terms of an arithmetic progression: Always a non-perfect square when p(a prime)=3 or p is congruent to 5 or 7 modulo 12
Konstantine Zelator
In a paper published by this author in www.academia.edu(see reference[3]), it was established that there exist no three positive integers which are consecutive terms of an arithmet…
Integer Solutions, Rational solutions of the equations x^4+y^4+z^4 -2(x^2)(y^2)-2(y^2)(z^2)-2(z^2)(x^2)=n and x^2+y^4+z^4-2x(y^2)-2x(z^2)-2(y^2)(z^2)=n; And Crux Mathematicorum Contest problem CC24
Konstantine Zelator
The subject matter of this work are the two equations: x^4+y^4+z^4-2(x^2)(y^2)-2(y^2)(z^2)-2(z^2)(x^2)= n (1) And x^2+y^4+z^4-2x(y^2)-2x(z^2)-2(y^4)(z^4)= n (2) where n is a natura…
The Diophantine equation xy=z^n; for n=2,3,4,5,6; the Diophantine equation xyz=w^2; and the Diophantine system: xy=v^2 and yz=w^2
Konstantine Zelator
In this work, we accomplish three goals. First, we determine the entire family of positive integer solutions to the three- variable Diophantine equation, xy=z^2; for n=2,3,4,5,6. F…
Integral points on rational curves of the form y=(x^2+bx+c)/(x+a); a,b,c integers
Konstantine Zelator
The subject matter of this work is the set of integral points(i.e. points with both coordinates integers) on the graphs of rational functions of the form f(x)=(x^2+bx+c)/(x+a), wit…
Integral regular truncated pyramids with rectangular bases and the diophantine equation x^2+y^2+z^2= t^2
Konstantine Zelator
A regular truncated pyramid with rectangular bases;consists of two rectangular bases whose centers are orthogonally aligned with respect to the parallel planes containing their bas…
Integral Triangles with one angle twice another, and with the bisector(of the double angle) also of integral length
Konstantine Zelator
Let ABC be a triangle with a,b,and c being its three sidelengths. In a 1976 article by Wynne William Wilson in the Mathematical Gazette(see reference[2]), the author showed that an…