# 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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### Simple question about dividing by 0, y=x/x when x=0

Is there a rule that says you have to simplify equations before evaluating them? Would y=x/x @ x=0 be 1 or undefined, since without reducing it, you'd divide by 0. I know the equation can simplify to ...
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### Prove divisibility with gcd

I have this math problem. The question is: Suppose that $a$ and $b$ are positive integers, with $d = \gcd(a, b)$. Suppose that there exists integers $r$ and $s$ so that $ar + bs= d$. We ...
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### Suppose that p,q are distinct odd primes. Suppose an integer k|pq-1 and k|lcm((p-1),(q-1)). Show that k|gcd((p-1),(q-1)).

I've spent ages looking at this problem and very little to show. Surely I would want to use the hypothesis that p and q are not equal. This would mean their gcd is 1. Any help would be greatly ...
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### Prove that $AB\mid CD$

I have this math question that I'm kind of confused on. This is the question: Let $A, B, C$ and $D$ be integers with $A \mid C$ and $B \mid D$ show that $$AB \mid CD.$$ I'm not 100% sure ...
212 views

### Proof that $n+k+3$ divides $n(n+1)(n+2)(n+3) - k(k+1)(k+2)(k+3)$.

I'm looking for proof that $$(n+k+3) \mid n(n+1)(n+2)(n+3) - k(k+1)(k+2)(k+3)\\ n,k \in \mathbb N^*, n>k$$ I tried using induction, but i'm not sure how it would work with 2 parameters.
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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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### Why are the disadvantages of approximation?

When I do 1/3 = 0.33333 but when I do 3*0.33333 then answer is 0.99999, I mean not whole 1 but 0.1 less than 1. What are the drawbacks of this think/rule since it's very basic math. Also why One cant ...
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### Prove that $GCD(a,b)=1$ if for all natural numbers $c, a|bc$ then $a|c$.

I'm trying to prove a theorem out of my text: Theorem: Let $a$ and $b$ be natural numbers. Then $GCD(a,b)=1$ if and only if for all natural numbers $c$, if $a|bc$ then $a|c$. I did come across this ...
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### If $n \mid a^2$, what is the largest $m$ for which $m \mid a$?

Given $n$, what is the largest $m$ such that $m \mid a$ for all $a$ with $n \mid a^2$? This is a generalization of if $40|a^2$ prove that $20|a$ when $a$ is an integer where $n=40$ and $m=20$. Here ...
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### Is my limited understanding of division and gcd on track?

Hello I am trying to make sense of some beginner theorems and propositions in number theory. I am wanting to also know if what I am saying is valid or just completely wrong. I am wanting to show that ...
A palindrome is a number that is the same when read forwards and backwards, such as $43234$. What is the smallest five-digit palindrome that is divisible by $11$? I'm probably terrible at math but ...