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 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
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Tag Archives: Diophantine Equation
A^2 = B^3 + C^3
Solve, given all unknowns are nonzero integers
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: