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On the diophantine equation pa + (p + 1)b = z2

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F15%3A50004086" target="_blank" >RIV/62690094:18470/15:50004086 - isvavai.cz</a>

  • Result on the web

    <a href="http://www.ijpam.eu/contents/2015-105-4/index.html" target="_blank" >http://www.ijpam.eu/contents/2015-105-4/index.html</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.12732/ijpam.v105i4.14" target="_blank" >10.12732/ijpam.v105i4.14</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    On the diophantine equation pa + (p + 1)b = z2

  • Original language description

    Recently, many papers have been devoted to the study of the Diophantine equation $x^a + y^b = z^2$ where $x, y$ are are positive integers and $a,b,z$ are non-negative integers.In this paper, we shall prove some results related to the equation $p^a+(p+1)^b=z^2$. In particular, we shall prove that there is no solution when $p>3$, $bgeq 2$ and $z$ even.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

  • Continuities

    S - Specificky vyzkum na vysokych skolach

Others

  • Publication year

    2015

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    International journal of pure and applied mathematics

  • ISSN

    1311-8080

  • e-ISSN

  • Volume of the periodical

    105

  • Issue of the periodical within the volume

    4

  • Country of publishing house

    BG - BULGARIA

  • Number of pages

    5

  • Pages from-to

    745-749

  • UT code for WoS article

  • EID of the result in the Scopus database