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Diophantine Equations of the form $x^2 - n y^2 = 1$

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#diophantine-equations #python
896
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Find all positive integers $a,b,c,x,y,z$ satisfying $a+b+c=xyz$ and $x+y+z=abc$.

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#elementary-number-theory #contest-math #systems-of-equations #diophantine-equations
166
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Infinitely many solutions of the equation $\frac{x+1}{y}+\frac{y+1}{x} = 4$

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#elementary-number-theory #diophantine-equations #fractions #pell-type-equations #vieta-jumping
74
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Find integers that satisfy $a^2b -2N = -c^2$

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#divisibility #diophantine-equations #integers
651
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Solving the following Diophantine equation: $m^2=n^5-5$

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#number-theory #diophantine-equations
79
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Find the positive integral values $n$ can take :${(x+y+z)}^2=nxyz$

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#elementary-number-theory #contest-math #diophantine-equations
102
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Discreteness of integer polynomials

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#number-theory #polynomials #diophantine-equations #integers #integer-lattices
136
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The diophantine equation $\dfrac1a=\dfrac{1}{x_1}+\dfrac{1}{x_2}+\cdots+\dfrac{1}{x_n}$ for arbitrary integer $n$.

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#elementary-number-theory #diophantine-equations
368
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Diophantine Equation Proof: solutions of $ax + by = dm$

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#number-theory #elementary-number-theory #diophantine-equations #linear-diophantine-equations
690
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Sieve for primes

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#number-theory #prime-numbers #diophantine-equations #sieve-theory
95
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Diophantine equation - power and multiplication

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#number-theory #elementary-number-theory #diophantine-equations #integers
222
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Diophantine equation power of 7 and 2

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#number-theory #elementary-number-theory #diophantine-equations #integers #exponential-diophantine-equations
90
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nonlinear Diophantine quadratic equations

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#number-theory #diophantine-equations
290
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Diophantine equation - Video explanation by Michael Penn

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#number-theory #elementary-number-theory #proof-explanation #diophantine-equations #intuition
74
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What manipulation is allowed when we solve a diophantine equation in $\mathbb{N}$?

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#elementary-number-theory #diophantine-equations

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