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FRUSTRATING SOLUTIONS FOR TWO EXPONENTIAL DIOPHANTINEEQUATIONS ℙa+ (ℙ+ 3)b − 1 = c

Sanjay Goyal

Page No. : 34-39

ABSTRACT

In this paper, two dissimilar exponential Diophantine equations ℙ^a+ ℙ+ 3^b− 1 = c²and(ℙ+ 1)^a − ℙ^b+ 1 = c²where ℙ= 2^p − 1 is a Mersenne prime for any prime p>2 anda, b, c∈Z⁺are deliberated and proved that0,2n,ℙ+ 3ⁿ,2n, 0, ℙⁿand 1,1, , n∈ℕsignifies solutions to the first equation and (2n, 0, (ℙ+ 1)ⁿ) and (2, 2, )embodies solutions to the later equation respectively.

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FRUSTRATING SOLUTIONS FOR TWO EXPONENTIAL DIOPHANTINEEQUATIONS ℙa+ (ℙ+ 3)b − 1 = c

ABSTRACT

FULL TEXT

Multidisciplinary Coverage