# Tagged Questions

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### $n \in \mathbb{N} \ 5|\ 2^{2n+1}+3^{2n+1}$

show for all $n \in \mathbb{N}$, $$5|\ 2^{2n+1}+3^{2n+1}$$ Indeed, we've to show that : $2^{2n+1}+3^{2n+1}=0[5]$ note that $2^{2n+1}+3^{2n+1}=2.4^n+3.9^n=$
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### Prove that if $n^2 - 1$ is divisible by a prime number $p$ such that $n - 1$ is not divisible by $p$, then $n + 1$ is also divisible by $p$.

If this proposition is false, please give at least $3$ counter-examples, and try to modify the proposition so that it becomes true. If the proposition is true, please try to prove this even more ...
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### Show that if $a=bq+r$ and $d|a$ and $d |b$, then $d|a-bq$

Show that if $a=bq+r$ and $d|a$ and $d |b$, then $d|a-bq$ That is show that if $d$ divides $a$ and $a=bq+r$ then $d$ divides $a-bq$. Here $d |a$ means "d divides a", that is $a=dk$ where ...
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### Prove that if $n+1$ is divisible by $m$ then $n^2-1$ is also divisible by $m$. [closed]

Prove that if $n+1$ is divisible by $m$ then $n^2-1$ is also divisible by $m$. And prove that if $n^2-1$ is divisible by $m$ then $n+1$ is also divisible by $m$.
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### Divisibility Problem: How can I solve this?

Suppose that $a,b,q,r$ are any integers such that $b > 0$ and $a = bq + r$, with $0\le r<b$, and suppose $b|a$. Must it be the case that $r = 0$? Justify your answer. Can anyone please let me ...
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### question about division algorithm described in handbook of applied crypto

http://cacr.uwaterloo.ca/hac/about/chap14.pdf#page=9 gives the following as a division algorithm: So step 1 is making it so that $yb^{n-t}$ is the same length as x and then step 2 loops until the ...
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### Long division: 24158 divided 6

Long division has always been a weakness of mine and some how I've gotten through school and sixth form without it, but i'd like to learn it, it's just that I have a problem with intuition. So I know ...
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### working out a percentage from my email open rates

i have the following numbers: recipients: $95$ opens: $39$ bounces: $2$ how would i get the percentage value per open? accoridng to this post: ...
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### Does half-life mean something can never completely decay?

Caffeine has a half-life of approximately six hours. I understand this to mean that every six hours, the amount of caffeine in the body is half of what it was six hours prior. Does that mean that ...
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### Notation for multiple of a number?

I've have a question about the notation for a multiple of a number, I know you can write it several ways: $2|4, 4 = 2n$ where $n$ is an integer, etc, but what about this one $$4 = \dot 2$$ I've ...
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### Euclidean Division to avoid need for floating point arithmetic

In simple terms (that Google has been unable to provide the answer), is there an approach to dividing a whole integer by a quotient & remainder? As a specific example, ...
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### How to generate two numbers such that the smaller divides the larger

I am creating a children's math game and need an algorithm (that I can write in JavaScript) to generate two numbers such that the smaller always divides the larger. How can I do that?
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### Factoring extremely large integers.

The question is about factoring extremely large integers but you can have a look at this question to see the context if it helps. Please note that I am not very familiar with mathematical notation so ...
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### If a number is divisible by a number, is it always divisible by that number's factors?

As the title says, if a number is divisible by a number, is it always divisible by that number's factors? An example being that $100$ is divisible by $20$, it is also divisible by $10, 5, 4, 2$ as ...
We all know how to recognize numbers that are multiple of $2, 3, 4, 5$ (and other). Some other divisors are a bit more difficult to spot. I am thinking about $7$. A few months ago, I heard a simple ...