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What are the necessary conditions on integers $a, b$ for the sum of the fractions below to be reduced?

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#elementary-number-theory #diophantine-equations
65
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Does ax+by = (a+b)z has a solution?

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#systems-of-equations #diophantine-equations
740
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How to solve the diophantine equation $x^2-x=y^3$

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#diophantine-equations
78
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Squaring an $n$ magic square

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#diophantine-equations #magic-square
2.1k
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Can a parallelogram have whole-number lengths for all four sides and both diagonals?

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#geometry #elementary-number-theory #diophantine-equations #polygons
480
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Solutions to diophantinte equation $x^4+2y^4=z^2$

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#number-theory #diophantine-equations
549
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For what $N$ does $N=x^3+y^3+z^3-2xyz$ have infinite integer solutions?

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#elementary-number-theory #diophantine-equations
2.4k
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How would one solve a linear equation in two integer variables?

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#elementary-number-theory #arithmetic #diophantine-equations #linear-diophantine-equations
57
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Find all triangles whose area is 1 and length of sides are all rational numbers.

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#functions #diophantine-equations #triangles
193
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Solutions to the equation $x^4+3y^4=z^2$

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#number-theory #diophantine-equations
68
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Integer solutions for $x^y=y^x$

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#number-theory #exponential-function #diophantine-equations
670
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Solve diophantine equation $x^4+4y^4=n$

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#diophantine-equations #prime-factorization
1.2k
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Diophantine equation of three variables

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#diophantine-equations
151
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How to get all natural solutions of the equation?

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#diophantine-equations
111
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Find all solutions to the diophantine equation

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#diophantine-equations

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