# Questions tagged [gcd-and-lcm]

Greatest common divisor and least common multiple are closely related notions in the integers and also make sense in certain other rings. The tag is intended to encompass all those questions.

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### Is it true that $\gcd(a+b,a+b-c)=1$ if $(a,b,c)=1$? [on hold]

Suppose $a$,$b$ and $c$ are three distinct positive integers which share no common divisor. Note that this implies that $a$, $b$, $c$ are pairwise coprime. Is it true that $\gcd(a+b,a+b-c)=1$ ...
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### A gcd problem from Niven's Introduction to the theory of numbers [duplicate]

Problem: If $(a, b) = 1$ and $p$ be an odd prime, prove that $$\left( a+b, \dfrac{a^p +b^p}{a+b} \right)=1 \quad \text{or} \quad 2$$ Source: An Introduction to the Theory of Numbers by Ivan Niven - ...
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### euclidean algorithm and linear combination for gcd

(i) Use the Euclidean Algorithm to find gcd(1253, 7930). (ii) Using the workings in (i), find m, n ∈ Z such that gcd(1253, 7930) = 1253m + 7930n. i) 7930 = 1253*6 + 412 1253 = 412*3 + 17 412 = 17*...
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