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Show that the numbers $(2n + 1)$ and $(4n^2+1)$ are relatively prime

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#elementary-number-theory #gcd-and-lcm
145
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$n>1$ is prime $\!\iff\!$ for all $a\!:\ (a,n)=1\,$ or $\,n\mid a$

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#elementary-number-theory #gcd-and-lcm
549
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Given an integer $a$, suppose $d=\gcd(3a+5,\,5a+7)>2$. Determine $d$.

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#elementary-number-theory #gcd-and-lcm
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Not able to understand the procedure used to find GCD of two numbers through Euclid's algorithm.

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#number-theory #euclidean-algorithm #gcd-and-lcm
74
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Given $n \in \Bbb Z$, determine $\gcd(3n^2 + 7n + 4, n + 2)$.

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#elementary-number-theory #polynomials #gcd-and-lcm
40
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Homomorphisms inbetween factor modules

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#linear-algebra #modules #transformation #gcd-and-lcm
613
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Properties of Greatest Common Divisors

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#elementary-number-theory #divisibility #gcd-and-lcm
51
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Exactly one solution to $ x\cdot a +y\cdot b = c $ with given $a,b \in \mathbb{N}\; c \in \mathbb{Z}$

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#elementary-number-theory #proof-writing #euclidean-algorithm #gcd-and-lcm
76
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Check for greatest common multiple in a range

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#elementary-number-theory #gcd-and-lcm
2.1k
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Show if $(a,p)=1$ there is a unique inverse of $a$ modulo $p$

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#modular-arithmetic #inverse #gcd-and-lcm
104
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If b and c are coprime, how to show that $(bx+cy, bc) = (b,y) (c,x)$?

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#elementary-number-theory #gcd-and-lcm
1.4k
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Proof verification: ab = gcd(a,b)lcm(a,b) without use of prime factorization

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#elementary-number-theory #proof-verification #gcd-and-lcm #least-common-multiple
276
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Cancellative Abelian Monoids

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#abstract-algebra #examples-counterexamples #monoid #least-common-multiple #gcd-and-lcm
51
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Cancellative Abelian Monoids II

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#abstract-algebra #monoid #least-common-multiple #gcd-and-lcm
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Why the $GCD$ of any two consecutive Fibonacci numbers is $1$?

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#elementary-number-theory #binomial-coefficients #divisibility #fibonacci-numbers #gcd-and-lcm

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