Question

For which positive integer $n$, is $\frac{2^n-1}{3}$ a factor of $4m^2+1$ for some integer $m$? (How to prove that one answer group is the only one?)

score 98 · Answer 1 · 2026-02-23 09:32:13

98

Views

For which positive integer $n$, is $\frac{2^n-1}{3}$ a factor of $4m^2+1$ for some integer $m$? (How to prove that one answer group is the only one?)

Published on 23 Feb 2026 - 9:32

score 198 · Answer 2 · 2026-02-23 09:33:46

198

Views

Integer solutions of $(2^{B_N}-1) \bmod \left( (-(3^N)) \bmod 2^{B_N}\right) =0$ other than $N\in \{1,2,3\} \{4,8,12\}$?

Published on 23 Feb 2026 - 9:33

score 352 · Answer 3 · 2026-02-23 09:32:06

352

Views

Finding all natural $x$, $y$, $z$ satisfying $7^x+1=3^y+5^z$

Published on 23 Feb 2026 - 9:32

score 62 · Answer 4 · 2026-02-23 09:34:50

62

Views

Exponential diophantine equation only need a single solution

Published on 23 Feb 2026 - 9:34

score 250 · Answer 5 · 2026-02-23 09:29:20

250

Views

Diophantine equation $2^x-3^y=2021$

Published on 23 Feb 2026 - 9:29

score 127 · Answer 6 · 2026-02-23 09:30:22

127

Views

Find a positive integer $i$ such that $9i + 1$ divides $2 \times 10^i - 1$

Published on 23 Feb 2026 - 9:30

score 46 · Answer 7 · 2026-02-23 09:27:41

46

Views

Can you prove mu-recursive functions are Diophantine without bounded universal quantifiers?

Published on 23 Feb 2026 - 9:27

score 613 · Answer 8 · 2026-04-08 16:26:23

613

Views

Pythagorean theorem in higher dimensions - with $n$th power in $n$ dimensions

Published on 08 Apr 2026 - 16:26

score 75 · Answer 9 · 2026-02-23 09:27:41

75

Views

Solution of the Diophantine equation

Published on 23 Feb 2026 - 9:27

score 340 · Answer 10 · 2026-02-23 09:29:57

340

Views

Solve over the positive integers: $7^x+18=19^y.$

Published on 23 Feb 2026 - 9:29

score 103 · Answer 11 · 2026-02-23 09:32:39

103

Views

For integers $m>2, n>1, c> 0$, with $2^m - 3^n=c$, does it follow for integers $x>0,y>0$ that $2^{m+x} - 3^{n+y} \ne c$

Published on 23 Feb 2026 - 9:32

score 162 · Answer 12 · 2026-02-23 09:30:43

162

Views

Establishing a lower bound with integers $m,n$ for $2^m - 3^n$ when $2^m > 3^n$

Published on 23 Feb 2026 - 9:30

score 523 · Answer 13 · 2026-02-23 09:29:20

523

Views

Collatz Conjecture: For a cycle where the maximum odd integer is $x_{max}$, does it follow that $x_{max} < 3^n$

Published on 23 Feb 2026 - 9:29

score 1.5k · Answer 14 · 2026-02-23 09:32:40

1.5k

Views

The number of solutions of $2^{2x}-3^{2y}=55$, in which $x$,$y$ are integers

Published on 23 Feb 2026 - 9:32

score 49 · Answer 15 · 2026-02-23 09:32:13

49

Views

The solutions of the diophantine equation $z^x=1+(z-1)y^2$

Published on 23 Feb 2026 - 9:32

List Question

For which positive integer $n$, is $\frac{2^n-1}{3}$ a factor of $4m^2+1$ for some integer $m$? (How to prove that one answer group is the only one?)

Integer solutions of $(2^{B_N}-1) \bmod \left( (-(3^N)) \bmod 2^{B_N}\right) =0$ other than $N\in \{1,2,3\} \{4,8,12\}$?

Finding all natural $x$, $y$, $z$ satisfying $7^x+1=3^y+5^z$

Exponential diophantine equation only need a single solution

Diophantine equation $2^x-3^y=2021$

Find a positive integer $i$ such that $9i + 1$ divides $2 \times 10^i - 1$

Can you prove mu-recursive functions are Diophantine without bounded universal quantifiers?

Pythagorean theorem in higher dimensions - with $n$th power in $n$ dimensions

Solution of the Diophantine equation

Solve over the positive integers: $7^x+18=19^y.$

For integers $m>2, n>1, c> 0$, with $2^m - 3^n=c$, does it follow for integers $x>0,y>0$ that $2^{m+x} - 3^{n+y} \ne c$

Establishing a lower bound with integers $m,n$ for $2^m - 3^n$ when $2^m > 3^n$

Collatz Conjecture: For a cycle where the maximum odd integer is $x_{max}$, does it follow that $x_{max} < 3^n$

The number of solutions of $2^{2x}-3^{2y}=55$, in which $x$,$y$ are integers

The solutions of the diophantine equation $z^x=1+(z-1)y^2$

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