Tagged Questions

This tag is for questions about divisibility, that is, determining when one thing is a multiple of another thing.

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LCM of $n$ consecutive natural numbers

Is there an efficient way to calculate the least common multiple of $n$ consecutive natural numbers? For example, suppose $a = 3$ and $b = 5$, and you need to find the LCM of $(3,4,5)$. Then the LCM ...
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How can I tell if a number in base 5 is divisible by 3?

I know of the sum of digits divisible by 3 method, but it seems to not be working for base 5. How can I check if number in base 5 is divisible by 3 without ...
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Let $a \in \Bbb Z$ such that $gcd(9a^{25}+10:280)=35$. Find the remainder of $a$ when divided by 70.

I'm stuck with this problem from my algebra class. We've recently been introduced to Fermat's little theorem and the Chinese Remainder Theorem. Let $a \in \Bbb Z$ such that $gcd(9a^{25}+10:280)=35$...
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prove if n - natural number divide number $34x^2-42xy+13y^2$ then n is sum of two square number

prove if n - natural number divide number $34x^2-42xy+13y^2$ where x,y are relatively prime then n is sum of two square number. I don't know what is going on in this exercise. I will be grateful ...
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Prove that if $n|5^n + 8^n$, then $13|n$ using induction

I have to prove using mathematical induction that if $n \ge 2$ and $n|5^n + 8^n$, then $13|n$. Please help me.
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why is area of a canvas being devided ?

Hey guy i am not so great at math and basically i have the following calculation that i need to figure out the entire formula ,looks like below: ...
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Prove that $3^{(q-1)/2} \equiv -1 \pmod q$ then q is prime number.

$q=2^m+1, m\ge 2$. Prove that if $$3^{(q-1)/2} \equiv -1 \pmod q$$ then q is prime number. I want to use if $q-1 | \phi(q)$, then q is prime number. But I don't know how to transform above equation. ...
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Have I discovered an analytic function allowing quick factorization?

So I have this apparently smooth, parametrized function: The function has a single parameter $m$ and approaches infinity at every $x$ that divides $m$. It is then defined for real $x$ apart ...
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Find all $(a,b) \in \Bbb Z^2$ such that $b \equiv 2a \pmod 5$ and $28a+10b=26$

I'm stuck with this exercise: Find all $(a,b) \in \Bbb Z^2$ such that $b \equiv 2a \pmod 5$ and $28a+10b=26$ It's from my algebra class, we are looking into diophantic and congruence equations. ...
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Proof for any natural n that: $8|5^n+2*3^{n-1}+1$

I used this method for proving this statement but I came up with a problem. $5^n+2*3^{n-1}+1 \equiv 1 + 25^{n/2} + 2 * 81^{(n-1)/4} \equiv 4 \pmod{8}$ What is the problem with my solution?
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Find all odd $n \in \mathbb{Z}^+$ such that $n\mid 3^n+1$.

Find all odd $n \in \mathbb{Z}^+$ such that $n\mid 3^n+1$. I believe that there doesn't exist any such $n$ except $1$. It is clear that $n$ can't be a multiple of $3$. Also, $3^n \equiv -1 \pmod n$. ...
Divisibility of $n^4 -n^2$ by 4 (induction proof)
We have to show that $$n^4 -n^2$$ is divisible by 3 and 4 by mathematical induction Proving the first case is easy however I do not know how what to do in the inductive step. Thank you.