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Questions tagged [coprime]

Use this tag for questions related to integers such that the only positive integer that divides them is 1.

In number theory, two integers are said to be coprime, relatively prime, or mutually prime if the only positive integer that divides both of them is 1. That is, the only common positive factor of the two numbers is 1. Equivalently, their greatest common divisor is 1.

273 questions
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Product of 2 coprime $a$ and $b$ both less than $n$ and both coprime to $n$ can never be $xn$ where $x$ is any positive integer

I am having trouble proving that product of two coprime $a$ and $b$ can never generate a number multiple of some greater number which is coprime to both $a$ and $b$.
Darshan
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to find co-prime with 7 from [-10,10]

How many integers in [-10,10] are co-prime with 7? I find that prime belongs to N, so my answer is 9(1,2,3,4,5,6,8,9,10). can you give me advice?
Jimmy
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Show that a positive integer $n \in N$ can be written as a sum of positive coprime integers with $gcd(a,b)=1 $

My idea was to show this via 3 cases. In case one n is even n=2k, k is odd In case two n is even with n=2k, k is odd In case three n is odd so n=2k+1 Then I have to show that for $n<7$ not every integer has a written form of $n=a+b; gcd(a,b)=1.$ I…
Andre
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Abstract solving congruence system when modules are not coprime

The following system is given $X \equiv a_1$ $mod$ $m_1$ $X \equiv a_2$ $mod$ $m_2$ such that $m_1, m_2 \in \mathbb{N} _{>1}$ and $m_1, m_2$ are not coprime. For which $a_1, a_2 \in \mathbb{Z} $ exists a solution for the system? I tried like this…
John
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How to find the number of coprime numbers to $100$?

Is there a way to find the number of coprime numbers ($2$ digit numbers) to $100$ without writing them?
thornton.sohan
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