
Recent Posts
 A^2 = B^3 + C^3
 Set {4,b,c,d,e} such that the product of any two of them increased by 1 is a square
 smallest integer whose first n multiples all contain a 3
 Set {3,b,c,d,e} such that the product of any two of them increased by 1 is a square
 Set {2,b,c,d,e} such that the product of any two of them increased by 1 is a square
Recent Comments
Archives
 February 2017
 January 2017
 December 2016
 November 2016
 October 2016
 September 2016
 August 2016
 July 2016
 June 2016
 May 2016
 April 2016
 March 2016
 February 2016
 January 2016
 December 2015
 November 2015
 October 2015
 September 2015
 August 2015
 July 2015
 June 2015
 May 2015
 April 2015
 March 2015
 February 2015
 January 2015
 December 2014
 November 2014
 October 2014
 September 2014
 August 2014
 July 2014
 June 2014
 May 2014
 April 2014
 March 2014
 February 2014
 January 2014
 December 2013
 November 2013
 October 2013
 September 2013
 August 2013
 July 2013
 June 2013
 May 2013
 April 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 July 2012
 June 2012
 May 2012
 April 2012
 March 2012
 February 2012
 January 2012
Categories
Meta
Tag Archives: Diophantine Equation
A^2 = B^3 + C^3
Solve, given all unknowns are nonzero integers Advertisements
x^2 + y^2 + z^2 = 3 xyz
Find 3 positive integers and which satisfy this equation: Using this solution, find a different solution by changing one and only one of the numbers. How many solutions does the equation have? … Continue reading
Diophantine equations : 2^A – 3^B = 3^D – 2^C
Find all the solutions to the Diophantine equations
a^n + b^n + c^n = x^n + y^n, n = 1,3
(1) Find a few solutions to the system where a, b, c, x, y are positive integers. (2) Prove that there are infinitely many solutions in positive integers, whose greatest common divisor … Continue reading
Diophantine equation : y^2 – p = 2^n, where p is a prime number
The diophantine equation where is a prime number < 100 The only solutions to the diophantine equation with y > 0 are given by (n, y) = … Continue reading
Diophantine equation : 2^a + 2^b + 2^c = x^2
Consider the Diophantine equation : for nonnegative integers,
Diophantine equation : (ab)/(a+b) + (bc)/(b+c) + (cd)/(c+d) + (da)/(d+a) = 0
Determine integral solutions of the Diophantine equation where are distinct Solutions: , , If , then , If , then , … Continue reading
Diophantine equation: (x – y – z)(x – y + z)(x + y – z) = 8 xyz
Does the Diophantine equation have an infinite number of relatively prime solutions? Solution: we have the trivial solutions and permutations thereof. For other solutions, note that each of the three equations is satisfied … Continue reading
Diophantine equation: (x – y – z)^3 = 27 xyz
Are there any integral solutions of the Diophantine equation other than or such that ? Solution: Let so that , or equivalently ……….. (1) since (1) … Continue reading
Diophantine Eq. : a^2 + b^2 + c^2 = 2d^2 and a^4 + b^4 + c^4 = 2d^4
Determine all integral solutions of the simultaneous Diophantine equations: