List questions from exponential-diophantine-equations

Published on 11 Apr 2023 - 2:08

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Find positive integer solutions for equation: $49^x + 7^{x-2} \cdot 3^{y+1} - 5 \cdot 9^y = 2023$.

Published on 17 May 2023 - 1:14

45

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Perfect power values taken by an Arithmetic Sequence

Published on 21 May 2023 - 4:30

46

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On an Exponential Diophantine Equation of the form $g^y = ax + b$

Published on 23 May 2023 - 14:34

117

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Are there non-trivial integer solutions for $3^x=2^y+1$?

Published on 25 Jul 2023 - 18:00

95

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$a^m + b^n = c^{m+n}$ general solution over integers

Published on 28 Jul 2023 - 20:35

23

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Method to Solve Exponential Diophantine equations of the type:$ \frac{1}{3} 2^l \left(\frac{1}{3} 2^{2 m-1} \left(2^{2 (3 n-1)}-1\right)-1\right)$

Published on 05 Sep 2023 - 13:28

637

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$x^y y^x$ in more than one way

Published on 02 Nov 2023 - 16:28

94

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Integer solutions for the equation $2r = q^{r-1}.$

Published on 03 Jan 2024 - 16:01

331

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Find all natural numbers $x,y,z$ such that $x^7+y^7=7^z$

Published on 18 Jan 2024 - 20:36

65

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Doubly exponential diophantine equation

Published on 10 Mar 2024 - 15:16

8.6k

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Finding $(a, b, c)$ with $ab-c$, $bc-a$, and $ca-b$ being powers of $2$

Published on 10 Jul 2015 - 9:06

1.1k

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Exponential Diophantine equation $7^y + 2 = 3^x$

Published on 29 Nov 2015 - 12:37

1.4k

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Solve : $\space 3^x + 5^y = 7^z + 11^w$

Published on 04 Apr 2013 - 10:38

322

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Exponential Diophantine Equation $3^x5^y-2^s7^t=1$.

Published on 23 Oct 2013 - 14:29

List Question

How do I solve the system $x^{x+y} = y^4$ and $y^{x + y} = x$ over the integers without guessing?

Find positive integer solutions for equation: $49^x + 7^{x-2} \cdot 3^{y+1} - 5 \cdot 9^y = 2023$.

Perfect power values taken by an Arithmetic Sequence

On an Exponential Diophantine Equation of the form $g^y = ax + b$

Are there non-trivial integer solutions for $3^x=2^y+1$?

$a^m + b^n = c^{m+n}$ general solution over integers

Method to Solve Exponential Diophantine equations of the type:$ \frac{1}{3} 2^l \left(\frac{1}{3} 2^{2 m-1} \left(2^{2 (3 n-1)}-1\right)-1\right)$

$x^y y^x$ in more than one way

Integer solutions for the equation $2r = q^{r-1}.$

Find all natural numbers $x,y,z$ such that $x^7+y^7=7^z$

Doubly exponential diophantine equation

Finding $(a, b, c)$ with $ab-c$, $bc-a$, and $ca-b$ being powers of $2$

Exponential Diophantine equation $7^y + 2 = 3^x$

Solve : $\space 3^x + 5^y = 7^z + 11^w$

Exponential Diophantine Equation $3^x5^y-2^s7^t=1$.

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