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JEŚMANOWICZ’ CONJECTURE ON PYTHAGOREAN TRIPLES
Bulletin of the Australian Mathematical Society, 2017In 1956, Jeśmanowicz conjectured that, for any positive integers $m$ and $n$ with $m>n$, $\gcd (m,n)=1$ and $2\nmid m+n$, the Diophantine equation $(m^{2}-n^{2})^{x}+(2mn)^{y}=(m^{2}+n^{2})^{z}$ has only the positive integer solution $(x,y,z)=(2,2,2)$. In this paper, we prove the conjecture if $4\nmid mn$ and $y\geq 2$.
Ma, Mi-Mi, Chen, Yong-Gao
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Generalized Pythagorean Triples
The College Mathematics Journal, 1985Penn State University in 1969. He is presently a professor of mathematics at the Germantown, Maryland Campus of Montgomery College. Prior to joining the Montgomery Col? lege faculty, he served on the mathematics faculties of Penn State University and the U. S. Naval Academy. He has also worked as a mathematician for the Computing Laboratory at Aberdeen
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The College Mathematics Journal, 1992
(1992). Primitive Pythagorean Triples. The College Mathematics Journal: Vol. 23, No. 5, pp. 413-417.
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(1992). Primitive Pythagorean Triples. The College Mathematics Journal: Vol. 23, No. 5, pp. 413-417.
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Mathematics Magazine, 1987
Let's call a solution of (1) in integers an Almost Pythagorean Triple (APT). In analytic geometry (1) represents a hyperboloid of revolution of one sheet, a doubly ruled surface. The tangent plane at a point cuts this surface in two straight lines called rulings.
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Let's call a solution of (1) in integers an Almost Pythagorean Triple (APT). In analytic geometry (1) represents a hyperboloid of revolution of one sheet, a doubly ruled surface. The tangent plane at a point cuts this surface in two straight lines called rulings.
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The Mathematics Teacher, 1959
An ancient problem continues to fascinate and challenge. High school students know about 3, 4, 5 right triangles. Do they know about 8, 15, 17 right triangles and 861, 620, 1061 right triangles?
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An ancient problem continues to fascinate and challenge. High school students know about 3, 4, 5 right triangles. Do they know about 8, 15, 17 right triangles and 861, 620, 1061 right triangles?
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Digits reversed Pythagorean triples
International Journal of Mathematical Education in Science and Technology, 1998A Pythagorean triple is called digits reversed if one integer in the triple has the same digits but in an inverse order with another. Some properties and many new examples of such triples are obtained. These results present a typical elementary example showing that new flowers are growing on the old mathematical land.
Sheng Jiang, Rui‐Chen Chen
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1997
Abstract The subject of this class is called number theory, which deals with the whole numbers, that is 1, 2, 3, 4 and so on and their negatives ‒1, ‒2, ‒3, …We shall not be interested in fractions or decimal numbers. This is a very old and beautiful subject but it is rather different from the way we do ordinary calculations for we ...
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Abstract The subject of this class is called number theory, which deals with the whole numbers, that is 1, 2, 3, 4 and so on and their negatives ‒1, ‒2, ‒3, …We shall not be interested in fractions or decimal numbers. This is a very old and beautiful subject but it is rather different from the way we do ordinary calculations for we ...
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Tabulating All Pythagorean Triples
Mathematics Magazine, 1978(1978). Tabulating All Pythagorean Triples. Mathematics Magazine: Vol. 51, No. 4, pp. 226-227.
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Semiperimeter and Pythagorean Triples
The American Mathematical Monthly, 2011We consider the semiperimeter (half the perimeter) of right triangles having relatively prime positive integers as side lengths.
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