[PDF] Top 20 All the Solutions of the Diophantine Equation $p^3 + q^2 = z^3$
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All the Solutions of the Diophantine Equation $p^3 + q^2 = z^3$
... 3p 2 + 3pT + T 2 = TA 2 (6) for some value A which guarantees that equality (3) is indeed a square q 2 = (TA) 2 ...3p 2 . The value T may assume all possible ... See full document
5
On the Solvability of the Diophantine Equation $p^x+(p+8)^y=z^2$ when $p>3$ and $p+8$ are Primes
... It follows then from (4) that + 7 is an even positive divisor (and non-trivial) of 2 @ , i.e., + 7 = 2 I where J is an integer such that 0 ≤ J < > . For J = 0 , we obtain that + 7 = 2 , which ... See full document
5
All the Solutions to an Open Problem of S. Chotchaisthit on the Diophantine Equation 2^x + p^y = z^2 when p are Particular Primes and y = 1
... that 2 divides at least one of the values (z – 3), (z + ...If 2 | (z– 3), then 2V = z – 3 or z = 2V + 3 implying that z + 3 = 2V ... See full document
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On the Ternary Quadratic Diophantine Equation $3(X^2+Y^2)-5XY=75 Z^2$
... quadratic equation given by 3 ( X 2 + Y 2 ) − 5 XY = 75 Z 2 is considered and searched for its many different integer ...integer solutions to the above equation are ... See full document
9
On the Cubic Diophantine Equation with Four Unknowns $x^2+y^2=z^3-w^3$
... integer solutions to the cubic equation with four unknowns given by x 2 + y 2 = z 3 − w 3 ...As Diophantine equations are rich in variety due to their definition, ... See full document
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All the Solutions of the Diophantine Equations (p + 1)^x – p^y = z^2 and p^y - (p + 1)^x = z^2 when p is Prime and x + y = 2, 3, 4
... The field of Diophantine equations is ancient, vast and no general method exists to decide whether a given Diophantine equation has any solutions, or how many solutions.. The literatur[r] ... See full document
5
On the Diophantine Equation ${(q^2 )^n }^x+p^y= z^2$ where q is any Prime Number and p is an Odd Prime Number
... the Diophantine equation + = has at most one solution for ...the Diophantine equation 4 + 7 = " # and 4 + 11 = " # have not any non-negative integer ... See full document
6
Solutions of the Diophantine Equation $2^x + p^y = z^2$ When $p$ is Prime
... = 2 and p is a Mersenne Prime, it has been established that 2 x + p 2 = z 2 has exactly 50 known ...Almost all of these solutions are achieved by a ... See full document
7
Integer Solution of the Homogeneous Bi-Quadratic Diophantine Equation with Five Unknowns $(x-y)(x^3-y^3)=(z^2-w^2)p^2$
... = z − w p is analyzed for its nonzero distinct integer ...integer solutions to the above bi-quadratic equation are ...the solutions and special number patterns namely polygonal and ... See full document
7
On Solutions of the Diophantine Equation $A^2-B^2 = Z^4$ when $A, B, Z$ are Positive Integers
... B, Z. We establish: (i) For all primes A, B, the equation has a unique ...+ 3 (N > 0) is prime, the equation has no ...+ 3 (N = 3a), the necessary and sufficient conditions ... See full document
5
On Solutions to the Diophantine Equation M^x+ (M + 6)^y = z^2 when M = 6N + 5
... investigate solutions to the title equation. We establish: (i) For all values M and even values x, y, then the equation has no ...the equation has a unique ...the equation has ... See full document
8
On the Homogeneous Ternary Quadratic Diophantine Equation 3(X+Y)2 2xy=12z2
... z is considered and searched for its many different integer ...integer solutions of the above equations are ...the solutions and special polygonal numbers are ... See full document
7
On Solutions to the Diophantine Equation $p^x + q^y = z^4$
... 2 2n + q = z 4 (3) implying that q = z 4 - (2 n ) 2 = (z 2 – 2 n )(z 2 + 2 n ...If q is prime, then z ... See full document
6
On Solutions of the Diophantine Equations $p^3 + q^3 = z^2$ and $p^3 - q^3 = z^2$ when p, q are Primes
... i.e., p + 2 = A 2 and p 2 – 2p + 4 = B 2 ...prime p, that p 2 – 2p + 4 is not a ...prime p for which p 2 – 2p + 4 = B 2 , and ... See full document
7
On Solutions to the Diophantine Equation 3^x + q^y = z^2
... y, z are positive integers and x + y = 2, 3, 4. When q > 3, the cases of infinitely many solutions, of a unique solution and of no-solutions are ...case q = ... See full document
5
On Solutions of the Diophantine Equation $p^x + q^y = z^2$
... The history of Diophantine Equations dates back to antiquity. There are endless varieties of Diophantine Equations, and there is no general method of solution. It is often asked how big are the gaps between ... See full document
7
Solutions of the Diophantine Equation $p^x + (p+6)^y = z^2$ when $p, (p + 6)$ are Primes and $x + y = 2, 3, 4$
... the Diophantine equation p x + (p+6) y = z 2 when p, (p + 6) are primes, and x, y, z are positive ...integers. All the six possibilities of x + y = ... See full document
6
On the Diophantine Equation $p^x + q^y = z^2$
... title equation has infinitely many solutions when p = 2 and also when p = ...prime p > 3, that the equation has a solution for each and every integer x ≥ ... See full document
5
On Solutions of the Diophantine Equations p^4 + q^4 = z^2 and p^4-q^4= z^2 when p and q are Primes
... of Diophantine equations is ancient, vast, and no general method exists to decide whether a given Diophantine equation has any solutions, or how many ... See full document
5
(Z) 3 Chloro N [(Z) 3 (3 chloro 2 methylphenylimino)butan 2 ylidene] 2 methylaniline
... There is a considerable interest in the development of new late transition metal catalysts for the polymerization of α - olefins since Brookhart discovered highly active α -diimine nickel catalysts (Johnson et al. , ... See full document
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