Question

Show the existence of infinitely many natural numbers $x$, $y$ such that $x(x+1)\mid y(y+1)$ but $x,x+1\not\mid y,y+1:$ how could we guess the hint?

score 131 · Answer 1 · 2023-07-02 09:40:42

Show the existence of infinitely many natural numbers $x$, $y$ such that $x(x+1)\mid y(y+1)$ but $x,x+1\not\mid y,y+1:$ how could we guess the hint?

score 19 · Answer 2 · 2026-03-28 20:08:12

19

Views

Let $y$ be a natural number of 4 digits that is represented in the decimal system as $y = x_1x_2x_3x_4$. If $3|(x_1 + x_2 + x_3 + x_4)$ then $3|y$.

Published on 28 Mar 2026 - 20:08

score 46 · Answer 3 · 2023-07-02 17:30:29

46

Views

Prove that if $p|ra-b$ and $p|rc-d$ then $p|(ad-bc)$ for $r\in \mathbb{Z}$

Published on 02 Jul 2023 - 17:30

score 86 · Answer 4 · 2023-07-04 18:59:01

86

Views

prove divisibility of a large number.

Published on 04 Jul 2023 - 18:59

score 60 · Answer 5 · 2026-03-28 04:35:54

60

Views

Proof with Error, if a|b and b|c then a|c since b =ak and c=bk so c=bk=(ak)k=ak^2

Published on 28 Mar 2026 - 4:35

score 309 · Answer 6 · 2026-03-30 06:31:22

309

Views

What numbers have a multiple that in base 10, can be written with only the digits $2$ and $5$.

Published on 30 Mar 2026 - 6:31

score 209 · Answer 7 · 2023-07-10 23:49:09

209

Views

The divisibility problem

Published on 10 Jul 2023 - 23:49

score 42 · Answer 8 · 2023-07-17 10:06:42

42

Views

Coincident products and coprime factors

Published on 17 Jul 2023 - 10:06

score 77 · Answer 9 · 2023-07-17 20:25:48

77

Views

Find all integer polynomials $f(x)$ such that $f(n)\mid 2^n-1$ for all $n\in\mathbb{N}^+$.

Published on 17 Jul 2023 - 20:25

score 82 · Answer 10 · 2026-03-25 14:36:43

82

Views

prime divisors of number of the form $32z^4+1$

Published on 25 Mar 2026 - 14:36

score 82 · Answer 11 · 2023-07-18 16:25:39

82

Views

Divisibility by 13 of a large number written in base 14

Published on 18 Jul 2023 - 16:25

score 102 · Answer 12 · 2023-07-18 16:41:28

102

Views

Divisibility of (a^n ± b^n) by (a ± b) for different values of 'n'

Published on 18 Jul 2023 - 16:41

score 40 · Answer 13 · 2026-03-30 15:13:15

40

Views

Specialized algorithms for edge cases of binary arithmetic

Published on 30 Mar 2026 - 15:13

score 32 · Answer 14 · 2023-07-20 14:44:18

32

Views

Errors in a proof in Stopple's book on analytic number theory

Published on 20 Jul 2023 - 14:44

score 85 · Answer 15 · 2026-04-02 01:31:56

85

Views

Find all functions over $\mathbb{Z}^+$ satisfying this divisibility criterion

Published on 02 Apr 2026 - 1:31

List Question

Show the existence of infinitely many natural numbers $x$, $y$ such that $x(x+1)\mid y(y+1)$ but $x,x+1\not\mid y,y+1:$ how could we guess the hint?

Let $y$ be a natural number of 4 digits that is represented in the decimal system as $y = x_1x_2x_3x_4$. If $3|(x_1 + x_2 + x_3 + x_4)$ then $3|y$.

Prove that if $p|ra-b$ and $p|rc-d$ then $p|(ad-bc)$ for $r\in \mathbb{Z}$

prove divisibility of a large number.

Proof with Error, if a|b and b|c then a|c since b =ak and c=bk so c=bk=(ak)k=ak^2

What numbers have a multiple that in base 10, can be written with only the digits $2$ and $5$.

The divisibility problem

Coincident products and coprime factors

Find all integer polynomials $f(x)$ such that $f(n)\mid 2^n-1$ for all $n\in\mathbb{N}^+$.

prime divisors of number of the form $32z^4+1$

Divisibility by 13 of a large number written in base 14

Divisibility of (a^n ± b^n) by (a ± b) for different values of 'n'

Specialized algorithms for edge cases of binary arithmetic

Errors in a proof in Stopple's book on analytic number theory

Find all functions over $\mathbb{Z}^+$ satisfying this divisibility criterion

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