Question

Find two integers $x$ and $y$ such that $15x+28y=1$

score 203 · Answer 1 · 2020-11-01 22:32:09

203

Views

Find two integers $x$ and $y$ such that $15x+28y=1$

Published on 01 Nov 2020 - 22:32

score 158 · Answer 2 · 2026-03-28 22:29:58

158

Views

Find gcd of $a = 170 + 32\sqrt{3}$ and $b = 61 + 35\sqrt{3}.$ Then find $f,g \in \mathbb{Z}[\sqrt{3}]$ such that $af + bg = d$ using norm function.

Published on 28 Mar 2026 - 22:29

score 313 · Answer 3 · 2020-11-08 10:44:40

313

Views

Show that $12n+5$ and $5n-2$ are relatively prime for all $n$ (in $\mathbb{Z}$)

Published on 08 Nov 2020 - 10:44

score 88 · Answer 4 · 2020-11-12 01:53:54

88

Views

Why is the gcd of $61+35\sqrt{3} $ and $170+32\sqrt{3}$ is $19 + 11\sqrt{3}$?

Published on 12 Nov 2020 - 1:53

score 69 · Answer 5 · 2020-11-13 03:09:58

69

Views

Euclidean Algorithm Failure

Published on 13 Nov 2020 - 3:09

score 38 · Answer 6 · 2026-03-28 12:18:39

38

Views

Linear Diophantine eq. in three variables

Published on 28 Mar 2026 - 12:18

score 117 · Answer 7 · 2020-11-16 13:20:44

117

Views

Find the smallest positive integer, whose last $4-digit$ part is $2010$ and is divisible by $2011$.

Published on 16 Nov 2020 - 13:20

score 501 · Answer 8 · 2020-11-16 15:49:42

501

Views

Finding HCF with the Euclidean Algorithm

Published on 16 Nov 2020 - 15:49

score 185 · Answer 9 · 2020-11-24 16:45:54

185

Views

for every K>1 and natural there is an arithmetic progression with coprime numbers, can't prove this

Published on 24 Nov 2020 - 16:45

score 81 · Answer 10 · 2020-11-27 04:24:08

81

Views

Determine the base and translate it to base 10.

Published on 27 Nov 2020 - 4:24

score 50 · Answer 11 · 2020-11-28 13:23:26

50

Views

Proof- division. Is it a true statement or false

Published on 28 Nov 2020 - 13:23

score 129 · Answer 12 · 2026-03-25 12:49:52

129

Views

$\begin{align}&(x\! -\! a,f_1(x),\ldots,f_r(x))\\ =\ &(x\! -\! a,f_1(a),\ldots,f_r(a))\end{align}\ $ [Ideal evaluation = mod reduction]

Published on 25 Mar 2026 - 12:49

score 109 · Answer 13 · 2020-12-05 02:39:52

109

Views

Generalization of Bezout Identity for Polynomials

Published on 05 Dec 2020 - 2:39

score 77 · Answer 14 · 2020-12-07 15:28:42

77

Views

GCD questions. How do I determine whether its true or false? (answer is true for both)

Published on 07 Dec 2020 - 15:28

score 1k · Answer 15 · 2020-12-10 03:24:11

1k

Views

Is a proof required for the Division Algorithm for polynomials?

Published on 10 Dec 2020 - 3:24

List Question

Find two integers $x$ and $y$ such that $15x+28y=1$

Find gcd of $a = 170 + 32\sqrt{3}$ and $b = 61 + 35\sqrt{3}.$ Then find $f,g \in \mathbb{Z}[\sqrt{3}]$ such that $af + bg = d$ using norm function.

Show that $12n+5$ and $5n-2$ are relatively prime for all $n$ (in $\mathbb{Z}$)

Why is the gcd of $61+35\sqrt{3} $ and $170+32\sqrt{3}$ is $19 + 11\sqrt{3}$?

Euclidean Algorithm Failure

Linear Diophantine eq. in three variables

Find the smallest positive integer, whose last $4-digit$ part is $2010$ and is divisible by $2011$.

Finding HCF with the Euclidean Algorithm

for every K>1 and natural there is an arithmetic progression with coprime numbers, can't prove this

Determine the base and translate it to base 10.

Proof- division. Is it a true statement or false

$\begin{align}&(x\! -\! a,f_1(x),\ldots,f_r(x))\\ =\ &(x\! -\! a,f_1(a),\ldots,f_r(a))\end{align}\ $ [Ideal evaluation = mod reduction]

Generalization of Bezout Identity for Polynomials

GCD questions. How do I determine whether its true or false? (answer is true for both)

Is a proof required for the Division Algorithm for polynomials?

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