| Title |
Pseudo-Heronian triangles whose squares of the lengths of one or two sides are prime numbers |
| Translation of Title |
Pseudo Herono trikampiai, kurių vienos arba dviejų kraštinių ilgių kvadratai – pirminiai skaičiai. |
| Authors |
Mazėtis, Edmundas ; Melničenko, Grigorijus |
| DOI |
10.15388/LMR.2021.25231 |
| Full Text |
|
| Is Part of |
Lietuvos matematikos rinkinys. Ser. B... Vilnius : Vilniaus universiteto leidykla. 2021, t. 62, p. 80-85.. ISSN 0132-2818. eISSN 2335-898X |
| Keywords [eng] |
Herono trikampis ; pseudo Herono trikampis ; pirminiai skaičiai ; dviejų sveikųjų skaičių kvadratų suma |
| Abstract [eng] |
The authors introduced the concept of a pseudo-Heron triangle, such that squares of sides are integers, and the area is an integer multiplied by $2$. The article investigates the case of pseudo-Heron triangles such that the squares of the two sides of the pseudo-Heron triangle are primes of the form $4k+1$. It is proved that for any two predetermined prime numbers of the form $4k+1$ there exist pseudo-Heron triangles with vertices on an integer lattice, such that these two primes are the sides of these triangles and such triangles have a finite number. It is also proved that for any predetermined prime number of the form $4k+1$, there are isosceles triangles with vertices on an integer lattice, such that this prime is equal to the values of two sides and there are only a finite number of such triangles. |
| Published |
Vilnius : Vilniaus universiteto leidykla |
| Type |
Journal article |
| Language |
Lithuanian |
| Publication date |
2021 |
| CC license |
|
