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AACS



International Transactions in Mathematical Sciences and Computer (ITMSC)




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1 On the Solutions of Exponential Diophantine Equation px + (p + 12)y = z2

Author: Satish kumar, Deepak Gupta and Hari Kishan,(Pages: 1-4)

Abstract:

In this paper, the solutions of Exponential Diophantine equation px + (p + 12)y = z2 has been discussed, where x, y, z are non-negative integers and p, p + 12 are primes such that p is of the form 6n + 1, where n is a natural number. We proved that this Exponential Diophantine equation has no non-negative integral solution.

Keyword:

Exponential Diophantine equations, Integral solutions, Pairs of prime of the form (p, p +12)

2 ON THE NON-LINEAR DIOPHANTINE EQUATION nx + (n + 4r)y = zm

Author: Satish Kumar, Sani Gupta, Hari Kishan,(Pages: 5-13)

Abstract:

We consider the non-linear Diophantine equation nx + (n + 4r)y = zm, m>2 where n ∈Z_O , r ∈N and x, y, z ∈Z^*. In this paper, we have showed that this Diophantine equation has no solution for all m if n is of the form n = 4k+1, where k ∈N.

Keyword:

Diophantine Equations, Exponential Equations, and Congruency Relation.

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