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$ax+by=c$ has unique solution for positive integers

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#elementary-number-theory #divisibility #diophantine-equations #gcd-and-lcm
135
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Diophantine Equation $a^3+b^3=22c^3$

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#elementary-number-theory #diophantine-equations
99
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Find the integer solution to when $15 × 2^n + 1$ is a perfect square?

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#number-theory #elementary-number-theory #diophantine-equations
84
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What is the complexity of solving this specific System of Diophantine Equations?

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#linear-algebra #number-theory #diophantine-equations #computational-complexity #linear-diophantine-equations
531
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How to solve this quadratic system of equations?

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#algebra-precalculus #polynomials #systems-of-equations #diophantine-equations
297
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Sum of Fibonacci Number and Product of Fibonacci Number are equal?

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#recurrence-relations #diophantine-equations #fibonacci-numbers #lucas-numbers
89
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Solutions of $(x^p - y^p)/(x - y) = z^p $

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#number-theory #prime-numbers #diophantine-equations #cyclotomic-polynomials
157
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When can $n$ be written as $a^2 +2b^2$?

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#number-theory #diophantine-equations #sums-of-squares
522
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Positive integer solutions to $x^2+y^2-z^2 = a^2, \;x^2+z^2-y^2 = b^2, \;y^2+z^2-x^2 = c^2$.

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#diophantine-equations #representations-by-quadratic-forms
99
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To find an isomorphism from a hyperplane in an ambient projective space to another projective space?

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#number-theory #algebraic-geometry #diophantine-equations #arithmetic-dynamics
140
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A diophantine equation of coprime integers

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#diophantine-equations #integers #coprime
64
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Given $x$, $y$, $z$ which are positive integers so that $(x+y)^4 + 5z = 63x$, find the value of $x+y+z$

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#number-theory #diophantine-equations
44
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Solution - or proof of no solution - for sum of squares starting from 0 equaling a square

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#diophantine-equations
135
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find the largest number that can't be written as $2008x+2009y+2010 z$

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#elementary-number-theory #modular-arithmetic #contest-math #diophantine-equations #gcd-and-lcm
32
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Solving a diophantine equation involing squares and a prime number

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#diophantine-equations

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