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 97 · Answer 1 · 2021-01-08 15:42:28

97

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 08 Jan 2021 - 15:42

score 197 · Answer 2 · 2021-01-27 14:04:29

197

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 27 Jan 2021 - 14:04

score 351 · Answer 3 · 2021-01-30 19:42:48

351

Views

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

Published on 30 Jan 2021 - 19:42

score 61 · Answer 4 · 2021-03-11 21:22:06

61

Views

Exponential diophantine equation only need a single solution

Published on 11 Mar 2021 - 21:22

score 249 · Answer 5 · 2021-03-26 14:25:46

249

Views

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

Published on 26 Mar 2021 - 14:25

score 126 · Answer 6 · 2021-04-07 18:04:09

126

Views

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

Published on 07 Apr 2021 - 18:04

score 45 · Answer 7 · 2021-04-26 14:38:51

45

Views

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

Published on 26 Apr 2021 - 14:38

score 611 · Answer 8 · 2021-04-26 21:22:00

611

Views

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

Published on 26 Apr 2021 - 21:22

score 74 · Answer 9 · 2021-05-01 14:58:55

74

Views

Solution of the Diophantine equation

Published on 01 May 2021 - 14:58

score 339 · Answer 10 · 2021-05-09 18:19:29

339

Views

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

Published on 09 May 2021 - 18:19

score 102 · Answer 11 · 2021-05-21 17:18:22

102

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 21 May 2021 - 17:18

score 161 · Answer 12 · 2021-05-29 08:33:29

161

Views

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

Published on 29 May 2021 - 8:33

score 522 · Answer 13 · 2021-06-06 04:31:45

522

Views

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

Published on 06 Jun 2021 - 4:31

score 1.5k · Answer 14 · 2021-06-15 08:58:27

1.5k

Views

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

Published on 15 Jun 2021 - 8:58

score 48 · Answer 15 · 2021-07-05 15:50:30

48

Views

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

Published on 05 Jul 2021 - 15:50

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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