AbstractIn this paper it has been proved that if q is an odd prime, q≢7 (mod 8), n is an odd integer ⩾5, n is not a multiple of 3 and (h,n)=1, where h is the class number of the filed Q(√−q), then the diophantine equation x2+q2k+1=yn has exactly two families of solutions (q,n,k,x,y)
summary:Let $\mathbb {Z}$, $ \mathbb {N}$ be the sets of all integers and positive integers, respect...
In this paper, all the solutions of the Diophantine equations x2 + 5a · pb = yn (for p = 29, 41) are...
In this paper, all the solutions of the Diophantine equations x2 + 5a · pb = yn (for p = 29, 41) are...
By factorizing the equation x2+2k=yn, n≥3, k-even, in the field Q(i), various theorems regarding the...
It has been proved that if p is an odd prime, y> 1, k ≥ 0, n is an integer greater than or equal ...
Abstract. In this paper, it has been proved that if n is an odd integer> 3 and h = 1 is the class...
gers and rational numbers respectively. Let D1, D2 ∈ N be odd, and let N(D1, D2) denote the number o...
AbstractLet D>2 be a positive integer, and let p be an odd prime not dividing D. In this paper, usin...
Let p be a fixed odd prime. Using certain results of exponential Diophantine equations, we prove tha...
Let q>3 denote an odd prime and d a positive integer without any prime factor p≡1(mod3). In this pap...
AbstractIn this note, we prove that the Diophantine equation 2m+nx2=yn in positive integers x, y, m,...
Diophantine equation is an equation in which solutions to it are from some predetermined classes and...
summary:Let $\mathbb {Z}$, $ \mathbb {N}$ be the sets of all integers and positive integers, respect...
summary:Let $\mathbb {Z}$, $ \mathbb {N}$ be the sets of all integers and positive integers, respect...
Erdős and Selfridge [7] proved that a product of consecutive integers can never be a perfect power....
summary:Let $\mathbb {Z}$, $ \mathbb {N}$ be the sets of all integers and positive integers, respect...
In this paper, all the solutions of the Diophantine equations x2 + 5a · pb = yn (for p = 29, 41) are...
In this paper, all the solutions of the Diophantine equations x2 + 5a · pb = yn (for p = 29, 41) are...
By factorizing the equation x2+2k=yn, n≥3, k-even, in the field Q(i), various theorems regarding the...
It has been proved that if p is an odd prime, y> 1, k ≥ 0, n is an integer greater than or equal ...
Abstract. In this paper, it has been proved that if n is an odd integer> 3 and h = 1 is the class...
gers and rational numbers respectively. Let D1, D2 ∈ N be odd, and let N(D1, D2) denote the number o...
AbstractLet D>2 be a positive integer, and let p be an odd prime not dividing D. In this paper, usin...
Let p be a fixed odd prime. Using certain results of exponential Diophantine equations, we prove tha...
Let q>3 denote an odd prime and d a positive integer without any prime factor p≡1(mod3). In this pap...
AbstractIn this note, we prove that the Diophantine equation 2m+nx2=yn in positive integers x, y, m,...
Diophantine equation is an equation in which solutions to it are from some predetermined classes and...
summary:Let $\mathbb {Z}$, $ \mathbb {N}$ be the sets of all integers and positive integers, respect...
summary:Let $\mathbb {Z}$, $ \mathbb {N}$ be the sets of all integers and positive integers, respect...
Erdős and Selfridge [7] proved that a product of consecutive integers can never be a perfect power....
summary:Let $\mathbb {Z}$, $ \mathbb {N}$ be the sets of all integers and positive integers, respect...
In this paper, all the solutions of the Diophantine equations x2 + 5a · pb = yn (for p = 29, 41) are...
In this paper, all the solutions of the Diophantine equations x2 + 5a · pb = yn (for p = 29, 41) are...
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