In this paper, we consider the non-linear Diophantine equations 61 x + 67 y = z 2 and 67 x + 73 y = z 2 , where x, y and z are non-negative integers. It has been shown that these non-linear Diophantine equations have no solution.
In this paper, we consider the non-linear Diophantine equation ௫ + ( + 6) ௬ = ݖ ଶ , where p and p+6 both are primes with p=6n+1. x, y and z are nonnegative integers and n is natural number. It is shown that this non-linear Diophantine equation has no solution.
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