Question

Let $S \subseteq \mathbb Z$, prove that if $0∈S$, and $k∈S$ implies $k+1∈S$ and $k-1∈S$, then $S=\mathbb Z$

score 105 · Answer 1 · 2016-10-06 07:13:25

105

Views

Let $S \subseteq \mathbb Z$, prove that if $0∈S$, and $k∈S$ implies $k+1∈S$ and $k-1∈S$, then $S=\mathbb Z$

Published on 06 Oct 2016 - 7:13

score 169 · Answer 2 · 2016-10-06 08:48:13

169

Views

Find integral solutions for surd problem

Published on 06 Oct 2016 - 8:48

score 119 · Answer 3 · 2016-10-07 10:32:37

119

Views

Karatsuba Multiplication - Wrong output when solving AD+BC

Published on 07 Oct 2016 - 10:32

score 4.7k · Answer 4 · 2016-10-12 03:59:13

4.7k

Views

if m, n are coprime which divide k then mn|k

Published on 12 Oct 2016 - 3:59

score 241 · Answer 5 · 2016-10-12 18:53:16

241

Views

Prove by cases that for all positive integers $n^n > n^{n-1}$

Published on 12 Oct 2016 - 18:53

score 317 · Answer 6 · 2026-03-29 14:25:31

317

Views

Prove that there is no positive integer $n$ for which $n^7-77$ is a Fibonnaci number.

Published on 29 Mar 2026 - 14:25

score 331 · Answer 7 · 2016-10-14 01:13:47

331

Views

Necessary and Sufficient Conditions for the pair of integers $\{m,n\}$ to generate $\mathbb{Z}$

Published on 14 Oct 2016 - 1:13

score 203 · Answer 8 · 2016-10-16 14:03:56

203

Views

Induction example, where base case harder to prove than inductive step

Published on 16 Oct 2016 - 14:03

score 93 · Answer 9 · 2026-03-28 00:06:00

93

Views

Show that product of integer polynomial values for arguments being complex roots of unity is integer.

Published on 28 Mar 2026 - 0:06

score 92 · Answer 10 · 2016-10-22 08:34:24

92

Views

If $x$ and $y$ are integers then prove that $(-x)+(-y)=-(x+y)$

Published on 22 Oct 2016 - 8:34

score 2k · Answer 11 · 2016-10-23 00:07:47

2k

Views

Prove that if $a$ and $b$ are some integers, then $a^2 - 4b$ does not equal $2$.

Published on 23 Oct 2016 - 0:07

score 1.1k · Answer 12 · 2016-10-23 05:15:30

1.1k

Views

How many integers $x$ satisfy: $-4<x^2+5x<14$?

Published on 23 Oct 2016 - 5:15

score 117 · Answer 13 · 2026-03-27 23:47:16

117

Views

A proof that $e$ or $\pi$ is irrational via algebraic integers

Published on 27 Mar 2026 - 23:47

score 69 · Answer 14 · 2016-10-27 10:29:22

69

Views

Find all such $b\in\mathbb{Z}_+$ that for all $n\in\mathbb{Z}_+$ there exists $y\in\mathbb{Z}_+$ such that $b^n+1=2y^3$

Published on 27 Oct 2016 - 10:29

score 225 · Answer 15 · 2016-10-28 06:22:22

225

Views

Provide an efficient algorithm for computing $(a + b \sqrt{3})^n$?

Published on 28 Oct 2016 - 6:22

List Question

Let $S \subseteq \mathbb Z$, prove that if $0∈S$, and $k∈S$ implies $k+1∈S$ and $k-1∈S$, then $S=\mathbb Z$

Find integral solutions for surd problem

Karatsuba Multiplication - Wrong output when solving AD+BC

if m, n are coprime which divide k then mn|k

Prove by cases that for all positive integers $n^n > n^{n-1}$

Prove that there is no positive integer $n$ for which $n^7-77$ is a Fibonnaci number.

Necessary and Sufficient Conditions for the pair of integers $\{m,n\}$ to generate $\mathbb{Z}$

Induction example, where base case harder to prove than inductive step

Show that product of integer polynomial values for arguments being complex roots of unity is integer.

If $x$ and $y$ are integers then prove that $(-x)+(-y)=-(x+y)$

Prove that if $a$ and $b$ are some integers, then $a^2 - 4b$ does not equal $2$.

How many integers $x$ satisfy: $-4<x^2+5x<14$?

A proof that $e$ or $\pi$ is irrational via algebraic integers

Find all such $b\in\mathbb{Z}_+$ that for all $n\in\mathbb{Z}_+$ there exists $y\in\mathbb{Z}_+$ such that $b^n+1=2y^3$

Provide an efficient algorithm for computing $(a + b \sqrt{3})^n$?

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