On the Diophantine Equations (๐‘ฅ1๐‘ฅ2๐‘ฅ3 โ€ฆ6)๐‘ฅ + (๐‘ฆ1๐‘ฆ2๐‘ฆ3 โ€ฆ1)๐‘ฆ = ๐‘ง2 and (๐‘ฅ1๐‘ฅ2๐‘ฅ3โ€ฆ4)2๐‘ฅ + (๐‘ฆ1๐‘ฆ2๐‘ฆ3 โ€ฆ2)5๐‘ฆ = ๐‘ง2

In this paper, the Diophantine equations (๐‘ฅ1๐‘ฅ2๐‘ฅ3โ€ฆ6)๐‘ฅ +(๐‘ฆ1๐‘ฆ2๐‘ฆ3โ€ฆ1)๐‘ฆ = ๐‘ง2 and (๐‘ฅ1๐‘ฅ2๐‘ฅ3โ€ฆ4)2๐‘ฅ + (๐‘ฆ1๐‘ฆ2๐‘ฆ3 โ€ฆ2)5๐‘ฆ = ๐‘ง2 have been discussed for positive integer solutions. Here ๐‘ฅ1,๐‘ฅ2,๐‘ฅ3 โ€ฆ and ๐‘ฆ1,๐‘ฆ2,๐‘ฆ3 โ€ฆ are digits 0, 1, 2,โ€ฆ9.

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Publication Details

Journal
International Journal of Mathematics Trends and Technology
Published
2025-05-31
DOI
https://doi.org/10.14445/22315373/ijmtt-v71i5p103
Primary Topic
Advanced Mathematical Theories and Applications
Type
article
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article

On the Diophantine Equations (๐‘ฅ1๐‘ฅ2๐‘ฅ3 โ€ฆ6)๐‘ฅ + (๐‘ฆ1๐‘ฆ2๐‘ฆ3 โ€ฆ1)๐‘ฆ = ๐‘ง2 and (๐‘ฅ1๐‘ฅ2๐‘ฅ3โ€ฆ4)2๐‘ฅ + (๐‘ฆ1๐‘ฆ2๐‘ฆ3 โ€ฆ2)5๐‘ฆ = ๐‘ง2

Smiti Aggarwal, Meenakshi Panchal
International Journal of Mathematics Trends and Technology
Advanced Mathematical Theories and Applications
article

On the Diophantine Equations (๐‘ฅ1๐‘ฅ2๐‘ฅ3 โ€ฆ6)๐‘ฅ + (๐‘ฆ1๐‘ฆ2๐‘ฆ3 โ€ฆ1)๐‘ฆ = ๐‘ง2 and (๐‘ฅ1๐‘ฅ2๐‘ฅ3โ€ฆ4)2๐‘ฅ + (๐‘ฆ1๐‘ฆ2๐‘ฆ3 โ€ฆ2)5๐‘ฆ = ๐‘ง2

Smiti Aggarwal, Meenakshi Panchal
article en

Abstract

In this paper, the Diophantine equations (๐‘ฅ1๐‘ฅ2๐‘ฅ3โ€ฆ6)๐‘ฅ +(๐‘ฆ1๐‘ฆ2๐‘ฆ3โ€ฆ1)๐‘ฆ = ๐‘ง2 and (๐‘ฅ1๐‘ฅ2๐‘ฅ3โ€ฆ4)2๐‘ฅ + (๐‘ฆ1๐‘ฆ2๐‘ฆ3 โ€ฆ2)5๐‘ฆ = ๐‘ง2 have been discussed for positive integer solutions. Here ๐‘ฅ1,๐‘ฅ2,๐‘ฅ3 โ€ฆ and ๐‘ฆ1,๐‘ฆ2,๐‘ฆ3 โ€ฆ are digits 0, 1, 2,โ€ฆ9.

International Journal of Mathematics Trends and TechnologyVol. 71(5)
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Advanced Mathematical Theories and Applications
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On the Diophantine Equations (๐‘ฅ1๐‘ฅ2๐‘ฅ3 โ€ฆ6)๐‘ฅ + (๐‘ฆ1๐‘ฆ2๐‘ฆ3 โ€ฆ1)๐‘ฆ = ๐‘ง2 and (๐‘ฅ1๐‘ฅ2๐‘ฅ3โ€ฆ4)2๐‘ฅ + (๐‘ฆ1๐‘ฆ2๐‘ฆ3 โ€ฆ2)5๐‘ฆ = ๐‘ง2 โ€” Smiti Aggarwal, Meenakshi Panchal ยท International Journal of Mathematics Trends and Technology (2025) | TGRS Research Map | TGRS