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[PDF] Top 20 Solutions of the Diophantine Equation $p^x + (p+6)^y = z^2$ when $p, (p + 6)$ are Primes and $x + y = 2, 3, 4$

Has 10000 "Solutions of the Diophantine Equation $p^x + (p+6)^y = z^2$ when $p, (p + 6)$ are Primes and $x + y = 2, 3, 4$" found on our website. Below are the top 20 most common "Solutions of the Diophantine Equation $p^x + (p+6)^y = z^2$ when $p, (p + 6)$ are Primes and $x + y = 2, 3, 4$".

Solutions of the Diophantine Equation $p^x + (p+6)^y = z^2$ when  $p, (p + 6)$  are Primes and  $x + y = 2, 3, 4$

Solutions of the Diophantine Equation $p^x + (p+6)^y = z^2$ when $p, (p + 6)$ are Primes and $x + y = 2, 3, 4$

... A prime gap is the difference between two consecutive primes. Numerous articles have been written on prime gaps, a very minute fraction of which is brought [5, 6] here. In 1849, A.de Polignac conjectured ... See full document

6

On Solutions to the Diophantine Equation  M^x+ (M + 6)^y = z^2 when M = 6N + 5

On Solutions to the Diophantine Equation M^x+ (M + 6)^y = z^2 when M = 6N + 5

... are primes and p = 6N + 1. It is shown [5] that the equation has no solutions, whereas in [7] particular cases of the equation are ...and solutions of this equation ... See full document

8

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

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

On Solutions to the Diophantine Equation 3^x + q^y = z^2

On Solutions to the Diophantine Equation 3^x + q^y = z^2

... prime, x, 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 ... See full document

5

On the Non-Homogeneous Quintic Equation with Five Unknowns $X^4-Y^4=10 p^3 (Z^2-W^2)$

On the Non-Homogeneous Quintic Equation with Five Unknowns $X^4-Y^4=10 p^3 (Z^2-W^2)$

... The theory of Diophantine equations offers a rich variety of fascinating problems [1-3]. Particularly, in [4-7] quintic equations with three unknowns are studied for their integral solutions. ... See full document

6

Integer Solution of the Homogeneous Bi-Quadratic Diophantine Equation with Five Unknowns $(x-y)(x^3-y^3)=(z^2-w^2)p^2$

Integer Solution of the Homogeneous Bi-Quadratic Diophantine Equation with Five Unknowns $(x-y)(x^3-y^3)=(z^2-w^2)p^2$

... integer solutions to the bi- quadratic equation with five unknowns ( ) x - y ( ) ( ) x 3 - y 3 = z 2 - w 2 p 2 ... See full document

7

On Solutions of the Diophantine Equations  
$p^3 + q^3 = z^2$  and  $p^3 - q^3 = z^2$  when   p,  q  are Primes

On Solutions of the Diophantine Equations $p^3 + q^3 = z^2$ and $p^3 - q^3 = z^2$ when p, q are Primes

... p - 2 = 3A 2 and p 2 +2p + 4 = 3B 2 (5) which must exist ...the equation p 3 - 2 3 = z 2 has no solutions as ... See full document

7

All the Solutions of the Diophantine Equation   $p^3 + q^2 = z^3$

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 Non-Homogeneous Quadratic Equation with Five Unknowns $x^2+xy-y^2-(z+w)=10 p^2$

On the Non-Homogeneous Quadratic Equation with Five Unknowns $x^2+xy-y^2-(z+w)=10 p^2$

... (i) y ( ) ( ) n − x n (ii) 3 [ p ( ) ( ) n , n − y n ] ...[ z ( ) ( ) α , β + w α , β ] = 5 y ( ) ( ) 4 β 22 x 10 α 2 ...3. ... See full document

8

On the Homogeneous Ternary Quadratic Diophantine Equation 3(X+Y)2 2xy=12z2

On the Homogeneous Ternary Quadratic Diophantine Equation 3(X+Y)2 2xy=12z2

... 3 xy  xy  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

Lattice Points Of A Cubic Diophantine Equation 11(X+Y)^2= 4(Xy+11z^3)

Lattice Points Of A Cubic Diophantine Equation 11(X+Y)^2= 4(Xy+11z^3)

... the Diophantine equations since its origins can be found in texts of the ancient Babylonians, Chinese, Egyptians, Greeks and so on [7 - ...of Diophantine equations is a treasure house in which the search ... See full document

6

On the Non-Homogeneous Ternary Quadratic Equation $2(x^2+y^2)-3xy+(x+y)+1=z^2$

On the Non-Homogeneous Ternary Quadratic Equation $2(x^2+y^2)-3xy+(x+y)+1=z^2$

... The Diophantine equation offer an unlimited field for due to their variety [ ] 1 − 3 ...[ 4 − 14 ] for quadratic equations with three ...quadratic equation with three unknowns given by ... See full document

7

A Ternary Quadratic Diophantine Equation $x^2+y^2=65z^2$

A Ternary Quadratic Diophantine Equation $x^2+y^2=65z^2$

... 7 x 23 y 2 = z 2 + z ( yx ) + 4 , International Journal of Latest Research in Science and technology, 2(2) (2013) ... See full document

7

On the Cubic Diophantine Equation with Five Unknowns x3 + y3 + (x+y)(x-y)2=32(z+w)p2

On the Cubic Diophantine Equation with Five Unknowns x3 + y3 + (x+y)(x-y)2=32(z+w)p2

... of Diophantine equations offers a rich variety of fascinating ...cubic equation with five unknowns given by x 3y 3  ( xy ) ( xy ) 2  ... See full document

5

Observation on the Cubic Diophantine Equation with Four Unknowns $(x^3+y^3)+(x+y)(x+y+1)=zw^2$

Observation on the Cubic Diophantine Equation with Four Unknowns $(x^3+y^3)+(x+y)(x+y+1)=zw^2$

... homogeneous Diophantine cubic equation is an interesting concept as it can be seen from [ 1 , 2 , 3 ] ...[ 4 − 11 ] a few special cases of cubic Diophantine equation with ... See full document

9

On the Ternary Quadratic Diophantine Equation $3(X^2+Y^2)-5XY=75 Z^2$

On the Ternary Quadratic Diophantine Equation $3(X^2+Y^2)-5XY=75 Z^2$

... 1. X ( ) α , 1 − t 16 , α + 77 ≡ 0 ( mod 11 ) 2. 9 Z ( ) ( ) α , 1 + Y α , 1 − t 38 , α ≡ 0 ( mod 23 ) ...7 Z ( ) ( ) α , 1 + X α , 1 − t 30 , α ≡ 0 ( mod 51 ) 4. Y ... See full document

9

On the Cubic Diophantine Equation with Four Unknowns $x^2+y^2=z^3-w^3$

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 ... See full document

11

Integral Solutions of Homogeneous Biquardratic
Equations with Five Unknowns $2(x^4-y^4)=(z^2-w^2)p^2$

Integral Solutions of Homogeneous Biquardratic Equations with Five Unknowns $2(x^4-y^4)=(z^2-w^2)p^2$

... of Diophantine Equations offer a rich variety of fascinating problems ...biquadratic Diophantine homogeneous and non-homogeneous have aroused the interest of numerous ...− 3 . In this context, one ... See full document

7

On Solutions of the Diophantine Equation  $p^x + q^y = z^2$

On Solutions of the Diophantine Equation $p^x + q^y = z^2$

... Numerous articles have been written on the Sophie Germain primes, as well as on the Twin primes. It is conjectured that there are an infinite number of: Twin prime pairs (p, p + 2), ... See full document

7

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

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

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