Question

Why is $ℤ$ defined as $ℤ := ℕ×ℕ \text{ / ~} $, where $ \text{~} := \{ [ (a,b),(c,d) ] | a+d = b+c \} $

score 113 · Answer 1 · 2019-06-30 01:15:11

113

Views

Why is $ℤ$ defined as $ℤ := ℕ×ℕ \text{ / ~} $, where $ \text{~} := \{ [ (a,b),(c,d) ] | a+d = b+c \} $

Published on 30 Jun 2019 - 1:15

score 220 · Answer 2 · 2026-03-25 23:36:40

220

Views

Expressing a positive integer as a sum of 3 positive integers

Published on 25 Mar 2026 - 23:36

score 360 · Answer 3 · 2019-07-01 15:54:13

360

Views

Why is 4 rare in the Van Eck sequence?

Published on 01 Jul 2019 - 15:54

score 330 · Answer 4 · 2019-07-02 13:32:36

330

Views

Show that $3^{7^n}+5^{7^n}\equiv 1 \pmod{7^{n+1}}$

Published on 02 Jul 2019 - 13:32

score 91 · Answer 5 · 2019-07-03 10:03:42

91

Views

How can we check if a system of equations accepts an integer solution?

Published on 03 Jul 2019 - 10:03

score 672 · Answer 6 · 2026-03-25 07:45:49

672

Views

Minimum possible value of $f(2007)$ where $f(m f(n)) = n f(m)$, $m,n\in \Bbb N$

Published on 25 Mar 2026 - 7:45

score 445 · Answer 7 · 2026-03-27 00:34:45

445

Views

All integer solutions to $x^2+y^2+z^2=2^{11}$?

Published on 27 Mar 2026 - 0:34

score 56 · Answer 8 · 2026-03-26 06:21:02

56

Views

Is there a specific terminology for numbers which are nontrivial multiples of triangular numbers?

Published on 26 Mar 2026 - 6:21

score 85 · Answer 9 · 2026-03-26 06:21:28

85

Views

What properties does the ratio of two triangular numbers $M$ and $N$ have, assuming $N \mid M$?

Published on 26 Mar 2026 - 6:21

score 845 · Answer 10 · 2026-03-26 23:11:26

845

Views

List of prime numbers in imaginary quadratic fields with UFD

Published on 26 Mar 2026 - 23:11

score 46 · Answer 11 · 2026-03-25 15:43:43

46

Views

When is $\sigma(q^{k-1})$ a square when $q \equiv 1 \pmod 4$ and $k \equiv 1 \pmod 4$?

Published on 25 Mar 2026 - 15:43

score 37 · Answer 12 · 2019-07-06 07:57:42

37

Views

A Function that could differentiate integers ($\in z^+$) from rest of positive real numbers

Published on 06 Jul 2019 - 7:57

score 115 · Answer 13 · 2019-07-07 01:53:29

115

Views

Properties of Two Inequalities

Published on 07 Jul 2019 - 1:53

score 1.1k · Answer 14 · 2019-07-08 09:41:50

1.1k

Views

How to prove that $x=y=1$ or $x=y=−1$ if $xy=1$?

Published on 08 Jul 2019 - 9:41

score 188 · Answer 15 · 2019-07-09 08:04:49

188

Views

Shorter way for writing expression

Published on 09 Jul 2019 - 8:04

List Question

Why is $ℤ$ defined as $ℤ := ℕ×ℕ \text{ / ~} $, where $ \text{~} := \{ [ (a,b),(c,d) ] | a+d = b+c \} $

Expressing a positive integer as a sum of 3 positive integers

Why is 4 rare in the Van Eck sequence?

Show that $3^{7^n}+5^{7^n}\equiv 1 \pmod{7^{n+1}}$

How can we check if a system of equations accepts an integer solution?

Minimum possible value of $f(2007)$ where $f(m f(n)) = n f(m)$, $m,n\in \Bbb N$

All integer solutions to $x^2+y^2+z^2=2^{11}$?

Is there a specific terminology for numbers which are nontrivial multiples of triangular numbers?

What properties does the ratio of two triangular numbers $M$ and $N$ have, assuming $N \mid M$?

List of prime numbers in imaginary quadratic fields with UFD

When is $\sigma(q^{k-1})$ a square when $q \equiv 1 \pmod 4$ and $k \equiv 1 \pmod 4$?

A Function that could differentiate integers ($\in z^+$) from rest of positive real numbers

Properties of Two Inequalities

How to prove that $x=y=1$ or $x=y=−1$ if $xy=1$?

Shorter way for writing expression

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