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    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)
    Email: N/A          DOI: N/A

    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)

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

    Author: Satish Kumar, Sani Gupta, Hari Kishan,(Pages: 5-13)
    Email: N/A          DOI: N/A

    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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    5 Economic Order Quantity Model for Deteriorating Products with Trade Credit and Partial Backlogging Considering Stock Dependant Demand

    Author: Dharmendra Yadav, S.R. Singh, Manisha Sarin ,(Pages: 15-23 )
    Email: dharmendrayadav3580@gmail.com          DOI: N/A

    Abstract:

    Inventory model with partial backlogging for deteriorating items is developed in this paper. Further, it is assumed that demand at the customer’s end is a function of stock. To boost the demand, trade credit policy is offered by the supplier. Here, holding cost is considered as the nonlinear function of stock level. Inventory model is investigated by considering that end stock level is negative. Feasibility of proposed model is analyzed with the help of numerical example. Sensitivity is also carried out with respect to important parameters.

    Keyword:

    Stock Dependent Demand, Variable Holding Cost, Partial Backlogging, Trade Credit

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