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Find all pairs $(m, n)$ of positive integers such that $m$ divides $8n+1$ and $n$ divides $8m+1$

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#number-theory #divisibility #diophantine-equations
141
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Quadratic residue

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#modular-arithmetic #diophantine-equations #quadratic-residues
49
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The system of Diophantine equations with same solution

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#systems-of-equations #diophantine-equations
91
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Is there a way to find positive values for unknown of Diophantine Equations?

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#linear-algebra #diophantine-equations #linear-diophantine-equations
243
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Can the solution to $n^2=pq+y^2$ help with the Golbach conjecture?

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#number-theory #elementary-number-theory #prime-numbers #diophantine-equations #goldbachs-conjecture
57
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Are the binomial coefficients unique?

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#diophantine-equations
354
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Infinitely many integer solutions of a cubic equation

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#recurrence-relations #algebraic-number-theory #diophantine-equations
49
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How do you solve $xy=8$ and $x^y=y^x$?

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#systems-of-equations #diophantine-equations
336
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Solve $a^3+b^3+3ab=1$ with $(a,b)\in \Bbb{Z}^2$

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#number-theory #diophantine-equations
74
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Is there better method than this one to solve quadratic diophantine equations?

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#number-theory #diophantine-equations #alternative-proof
82
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Do there exist (non-trivial) prime solutions to the equations $p^2 = 1$ mod $q$, $q = 1$ mod $p$?

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#group-theory #finite-groups #modular-arithmetic #diophantine-equations #sylow-theory
90
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All natural number solutions of the equation

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#algebra-precalculus #elementary-number-theory #diophantine-equations
292
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Solve the diophantine equation 71x +29y = 101

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#diophantine-equations
59
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Solve the equation below for all m and n which are positive integers

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#diophantine-equations
251
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Number of integral solutions to elliptic curve $\binom n2=\binom m3$.

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#combinatorics #binomial-coefficients #diophantine-equations #elliptic-curves

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