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Diophantine equation $x^{y} - y^{x}=1$.

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#elementary-number-theory #diophantine-equations #perfect-powers
4.2k
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Diophantine equation $x^2 + y^2 = z^3$

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#number-theory #diophantine-equations
297
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Quartic diophantine equation: $16r^4+112r^3+200r^2-112r+16=s^2$

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#diophantine-equations #problem-solving
333
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On the complete solution to $x^2+y^2=z^k$ for odd $k$?

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#number-theory #diophantine-equations #parametric
87
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Help solving the quadratic equation $ax^2-4bx+4bc-\frac{d^2}{a}=0$

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#soft-question #diophantine-equations #quadratics
1.3k
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find all integers $a,b,c$ such that $a^2=bc+1,$ $b^2=ca+1.$

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#number-theory #diophantine-equations
261
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Find $a$, $b$ and $c$ that satisfy the following equations

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#diophantine-equations #systems-of-equations
202
Views

Diophantine equation $x^2+y^2=z^2+t^2$?

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#elementary-number-theory #diophantine-equations #sums-of-squares
86
Views

Solve $a^n - b^n = 8$ with $a,b \in \mathbb{Z}$ and $n \in \mathbb{N}_{\geq 2}$.

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#number-theory #diophantine-equations
56
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Solutions of diophantine equation: $s^2 = (ad)^2+ (bc-ad+4ac)^2$

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#diophantine-equations #recreational-mathematics #problem-solving
144
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If $a_{n+1}=\frac {a_n^2+5} {a_{n-1}}$ then $a_{n+1}=Sa_n+Ta_{n-1}$ for some $S,T\in \Bbb Z$.

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#sequences-and-series #recurrence-relations #diophantine-equations
149
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Rational solutions $(a,b)$ to the equation $a\sqrt{2}+b\sqrt{3} = 2\sqrt{a} + 3\sqrt{b}$

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#number-theory #diophantine-equations #rational-numbers
477
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Finding the integer solutions of $y^2 = x^3 - 12$

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#number-theory #diophantine-equations
319
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On products of ternary quadratic forms $\prod_{i=1}^3 (ax_i^2+by_i^2+cz_i^2) = ax_0^2+by_0^2+cz_0^2$

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#number-theory #algebraic-number-theory #diophantine-equations #quadratic-forms
38
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In $x^2(y-2)-x(y-4)=2^{z+1}-2$ for a given $y$, how many solutions $x,z$ are possible?

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#algebra-precalculus #diophantine-equations

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