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Solve $ x^2 + xy + y^2 = \left( \frac{x+y}{3}+1 \right)^2 $ in integers

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#number-theory #diophantine-equations
765
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No integers satisfying $x^2+2y^2 = p$

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#number-theory #modular-arithmetic #diophantine-equations
90
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Can anyone help me in determining the value of a,b and c?

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#systems-of-equations #diophantine-equations #symmetric-polynomials
105
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On the greatest integer that cannot be expressed as $c_{1}a_{1}+c_{2}a_{2}$

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#algebra-precalculus #number-theory #diophantine-equations
130
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Conjecture: Is the identity $2^5-5^2=2+5$ unique?

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#elementary-number-theory #diophantine-equations #conjectures
880
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Solve $ab + cd = -1; ac + bd = -1; ad + bc = -1$ over the integers

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#systems-of-equations #diophantine-equations #integers
119
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Find all the integer solutions involving the Diophantine-equation $\frac{x+ y}{x^{2}+ y^{2}+ xy}= \frac{5}{19}$ .

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#divisibility #diophantine-equations #discriminant
99
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Cyclic Remainders

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#number-theory #elementary-number-theory #modular-arithmetic #divisibility #diophantine-equations
180
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Solving the diophantine equation $x^3+y^3 = z^6+3$

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#elementary-number-theory #diophantine-equations
67
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Discuss a set of three numbers $x, y, z ∈ N$ such that $x^2+5^4=5^y+z$

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#diophantine-equations
198
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Rational points on $2x^2+2y^2=1$ and integral solutions to $2X^2+2Y^2=Z^2$

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#elementary-number-theory #diophantine-equations
82
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How to solve $y^3=x(x+1)$ where $x$ and $y$ are integers?

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#elementary-number-theory #divisibility #diophantine-equations #gcd-and-lcm
276
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Diophantine equation: $n^2=c(4ab-a-b)-b$?

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#number-theory #elementary-number-theory #prime-numbers #diophantine-equations
403
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A difficult Diophantine equation

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#number-theory #diophantine-equations
159
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Finding all the integer solutions

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#number-theory #elementary-number-theory #polynomials #diophantine-equations #integers

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