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Research Article

EEO. 2020; 19(1): 472-475


ON THE NON-LINEAR DIOPHANTINE EQUATION 𝒑𝒙 + (𝒑 + 𝟐)𝒚 = 𝒛𝟐

*Sani Gupta, Rajiv Kumar, Satish Kumar.




Abstract

: In this paper, we consider the non-linear Diophantine equation
𝑝𝑥+ (𝑝 + 2)𝑦 = 𝑧2 … (1)
Where p and p+2 are twin primes and x, y and z are positive integers with zero. We find that the equation (1) has infinite solutions (p, x, y, z) = ( 6n-1, 1, 1, 2 3𝑛 ) for some natural numbers n and other possible solution (3, 1, 0, 2,) of equation (1) also considered.

Key words: Diophantine Equations, Exponential Equations, Congruency Relation, Twin Prime






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