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pro vyhledávání: '"Zelator, Konstantine \\'Hermes\\'"'
Autor:
Zelator, Konstantine "Hermes"
In his book "250 Problems in Elementary Number Theory", W.Sierpinski shows that the numbers 1+2^(2^n)+2^(2^n+1) are divisible by 21; for n=1,2,.... In this paper, we prove a similar but more general result.Consider the natural numbers of the form I(n
Externí odkaz:
http://arxiv.org/abs/0806.1514
Autor:
Zelator, Konstantine "Hermes"
Even though four theorems are actually proved in this paper, two are the main ones,Teorems 1 and 3. In Theorem 1 we show that if a and be are odd squarefree positive integers satisfying certain quadratic residue conditions; then there exists no primi
Externí odkaz:
http://arxiv.org/abs/0805.1052
Autor:
Zelator, Konstantine "Hermes"
Given a right triangle ABC, with the ninety degree angle at A; consider the triangle O1OO2.Where the point O is the midpoint of the hypotenuseBC(and so the center of the triangle ABC's circumcircle), the point O1 being the triangle AOB's circumcenter
Externí odkaz:
http://arxiv.org/abs/0804.1340
Autor:
Zelator, Konstantine "Hermes"
We prove that for given integers b and c, the diophantine equation x^2+bx+c=y^2, has finitely many integer solutions(i.e. pairs in ZxZ),in fact an even number of such solutions(including the zero or no solutions case).We also offer an explicit descri
Externí odkaz:
http://arxiv.org/abs/0803.3956
Autor:
Zelator, Konstantine "Hermes"
There are four characteristic circles for each triangle on a plane. All for are tangential to the three straight lines containing the triangles' three sides. Three are exterior circles, the fourth is the in-circle. When the triangle is Pythagorean, t
Externí odkaz:
http://arxiv.org/abs/0803.3605
Autor:
ZELATOR, KONSTANTINE 'HERMES'1
Publikováno v:
Mathematical Spectrum. 2010/2011, Vol. 43 Issue 1, p9-13. 5p.
Given a right triangle ABC, with the ninety degree angle at A; consider the triangle O1OO2.Where the point O is the midpoint of the hypotenuseBC(and so the center of the triangle ABC's circumcircle), the point O1 being the triangle AOB's circumcenter
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4b9ba7fe18b8a0ffbec870276b2b178c
http://arxiv.org/abs/0804.1340
http://arxiv.org/abs/0804.1340
There are four characteristic circles for each triangle on a plane. All for are tangential to the three straight lines containing the triangles' three sides. Three are exterior circles, the fourth is the in-circle. When the triangle is Pythagorean, t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2afec46039b51feed94fa66d624e369a
http://arxiv.org/abs/0803.3605
http://arxiv.org/abs/0803.3605
In his book "250 Problems in Elementary Number Theory", W.Sierpinski shows that the numbers 1+2^(2^n)+2^(2^n+1) are divisible by 21; for n=1,2,.... In this paper, we prove a similar but more general result.Consider the natural numbers of the form I(n
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::30bf8b7fb7286b0763cc3f159608e33b
Even though four theorems are actually proved in this paper, two are the main ones,Teorems 1 and 3. In Theorem 1 we show that if a and be are odd squarefree positive integers satisfying certain quadratic residue conditions; then there exists no primi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fca851dbdef712253a5e369bbb4acced