Question

Exactly one solution to $ x\cdot a +y\cdot b = c $ with given $a,b \in \mathbb{N}\; c \in \mathbb{Z}$

score 50 · Answer 1 · 2015-04-29 15:53:17

50

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Exactly one solution to $ x\cdot a +y\cdot b = c $ with given $a,b \in \mathbb{N}\; c \in \mathbb{Z}$

Published on 29 Apr 2015 - 15:53

score 146 · Answer 2 · 2015-04-30 03:39:48

146

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Polynomials and Euclidean algorithm

Published on 30 Apr 2015 - 3:39

score 2.2k · Answer 3 · 2015-04-30 23:05:12

2.2k

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Find the gcd of polynomials

Published on 30 Apr 2015 - 23:05

score 1.6k · Answer 4 · 2015-05-01 21:33:05

1.6k

Views

Let $R$ be a Euclidean domain with degree function $\varphi$ and $R$ not a field. If $a \ne 0$ and $b \ne 0$ be two elements in $R$...

Published on 01 May 2015 - 21:33

score 117 · Answer 5 · 2015-05-08 05:39:04

117

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Consider the number $N=2015^{2015}$. What is the remainder of $N$ when it is divided by $4$? $11$? $44$?

Published on 08 May 2015 - 5:39

score 4.1k · Answer 6 · 2015-05-09 18:30:49

4.1k

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Prove that Euclid's algorithm computes the GCD of any pair of nonnegative integers

Published on 09 May 2015 - 18:30

score 46 · Answer 7 · 2015-05-10 02:59:25

46

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Find a pair of polynomials $a(x)$ and $b(x)$ so that $a(x)+b(x)=x^6 -1$ and the $\gcd(a(x),b(x))=x+1$.

Published on 10 May 2015 - 2:59

score 363 · Answer 8 · 2015-05-10 23:47:13

363

Views

Greatest common divisor of two numbers $a$ and $b$

Published on 10 May 2015 - 23:47

score 1.7k · Answer 9 · 2015-05-16 02:53:39

1.7k

Views

Why 9 mod -7 = -5? Quotient and remainder with negative integers.

Published on 16 May 2015 - 2:53

score 556 · Answer 10 · 2015-05-17 12:29:25

556

Views

Using Bezout's identity

Published on 17 May 2015 - 12:29

score 43 · Answer 11 · 2015-05-20 09:33:15

43

Views

If the euclidean algorithm is used to solve an equation ( i.e., $ax = b \mod(z)$) is the solution unique?

Published on 20 May 2015 - 9:33

score 92 · Answer 12 · 2015-05-24 12:09:49

92

Views

How to proceed with Euclidean algorithm for finding greatest common divisor of two polynomials.

Published on 24 May 2015 - 12:09

score 72 · Answer 13 · 2015-06-01 11:47:05

72

Views

a question on gcd of 2 rational integers being 1 and euclid's lemma

Published on 01 Jun 2015 - 11:47

score 2.3k · Answer 14 · 2015-06-03 09:33:38

2.3k

Views

Extended Euclidean Algorithm with negative numbers minimum non-negative solution

Published on 03 Jun 2015 - 9:33

score 1.2k · Answer 15 · 2015-06-04 16:22:44

1.2k

Views

Why does the largest $x$ such that $a$, $b$ divided by $x$ leave the same remainder equal $a-b$?

Published on 04 Jun 2015 - 16:22

List Question

Exactly one solution to $ x\cdot a +y\cdot b = c $ with given $a,b \in \mathbb{N}\; c \in \mathbb{Z}$

Polynomials and Euclidean algorithm

Find the gcd of polynomials

Let $R$ be a Euclidean domain with degree function $\varphi$ and $R$ not a field. If $a \ne 0$ and $b \ne 0$ be two elements in $R$...

Consider the number $N=2015^{2015}$. What is the remainder of $N$ when it is divided by $4$? $11$? $44$?

Prove that Euclid's algorithm computes the GCD of any pair of nonnegative integers

Find a pair of polynomials $a(x)$ and $b(x)$ so that $a(x)+b(x)=x^6 -1$ and the $\gcd(a(x),b(x))=x+1$.

Greatest common divisor of two numbers $a$ and $b$

Why 9 mod -7 = -5? Quotient and remainder with negative integers.

Using Bezout's identity

If the euclidean algorithm is used to solve an equation ( i.e., $ax = b \mod(z)$) is the solution unique?

How to proceed with Euclidean algorithm for finding greatest common divisor of two polynomials.

a question on gcd of 2 rational integers being 1 and euclid's lemma

Extended Euclidean Algorithm with negative numbers minimum non-negative solution

Why does the largest $x$ such that $a$, $b$ divided by $x$ leave the same remainder equal $a-b$?

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