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Questions tagged [natural-numbers]

For question about natural numbers $\Bbb N$, their properties and applications

In mathematics, the natural numbers are those used for counting ("there are six coins on the table") and ordering ("this is the third largest city in the country"). These purposes are related to the linguistic notions of and , respectively (see English numerals). A later notion is that of a nominal number, which is used only for naming.

Properties of the natural numbers related to , such as the distribution of , are studied in . Problems concerning counting and ordering, such as partition enumeration, are studied in .

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Construction of natural numbers with composition.

If $f(x)=px $ then $ff(x)=p^{2}x$ ,$fff(x)=p^{3}x $ and so on. The n-1 composition raises p to the power n. If 0 exists, then we can obtain 1. From 1, we can obtain 2 and so on.Can we define natural numbers as the exponent of p in $f(x)=px$. Can we…
Aristotle Stagiritis
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exam question that i could not do

How many natural numbers less than 1000 are divisible by 5 or 7 but NOT by 35? (a) 285 (b) 313 (c)341 (d) 243 i know that numbers upto 1000 that are divisible by 5 are 1000/5=200 and by 7 are 142. so total numbers that are divisible by 5 or 7 =342.…
Manish Kumar Balayan
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If the digit sum function would be valid for base 1, would it mean that the digit sum of n in base 1 be equal n?

Let us define $n \in \mathbb{N} \setminus \{0\}$ and let us define the digit sum function for the base $b$ as $F_b(n)$ (according to wikipedia). Also as mentioned in the previous wikipedia link the base is $b \ge 2$. What I am asking myself is if…
PiMathCLanguage
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If $a|N$ and $b|N$ where $a,b$ are coprime , is it necessary that $(a \times b) |N$?

In the above statement N , a , b are natural numbers . I was wondering whether the above statement is always true . If it is always true will anyone give me a simple reason or proof for it ? Please guide me .
Sameer Nilkhan
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Given $a^2+b^3=c^4+d^5$, prove a+b+c+d is even (for natural numbers)

All I can say is that either all numbers are odd, all numbers are even, or exactly two of them are even. How will a proof of that go?
aradarbel10
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Is $0$ included as an element of the natural numbers?

I've seen a lot of contradictory information online when it comes to if $0 \in \mathbb{N}$ and I've been wanting to know if there's a definite answer to this or not. Any help is greatly appreciated.
Aussie Mathematician
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How to prove rounded any real number multiplied by natural number consists of combinations of integer part of real number

$n,i,j \in\mathbb{N}$ $r \in \mathbb{R^{+}}$ $k = \left \lfloor{r}\right \rfloor $ (integer part of $r$) $round ()$ = round function to make an integer $round (n \times r) = ik + j(k+1)$ For example, Assume that $n = 8$, $r = 3.2$, then $round(8…
Min-Uk Kim
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How can I interpret the numbers for count correctly

I know that the numbers we use to identify a group by its quantity, the natural numbers we use for it, we have tens, hundreds, units, milli million ... etc 1 is like O 2 is like OO 3 is like OOO 4 is like OOOO 5 is like OOOOO 6 is like OOOOOO 7 is…
user686724
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Proof that square of sum equal to sum of cubes of N.

Does exist a proof for this: $$(1 + 2 + 3 + 4)^2=1^3 + 2^3 + 3^3 + 4^3$$
Josef Klimuk
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What is the relationship between any natural number and two other natural numbers?

By this I mean, you could take any natural number, apply some kind of operation (arithmetic or other), and end up with two natural numbers. Then, you can apply an inverse operation on the two produced natural numbers to produce the original natural…
John
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How to solve for the sides of a rectangle whose sides are natural numbers given its area is a known natural number?

This may not be the best way to formulate the question but I am looking for a method to solve the following equation $d \cdot n'=n$ where $d, n', n \in \mathbb{N}$ and $n \neq1$ is known. How should I approach this problem? Are there guaranteed…
ClimbingTheCurve
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proving that f:N^2->N is bijective

I'v got a function $f:\omega^2\to\omega$ defined $$ f(n,k)=\frac{\left(n+k+1\right)\left(n+k\right)}{2}+n $$ This function suppose to be a bijection between $\omega$ and $\omega^2$, but I can't find a simple proof that it's bijective. $f$ noppose to…
Barak Ohana
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Determine with a proof the largest number which can be written as a product of natural numbers which have sum 2012

I'm having trouble finding the largest number and proving it.
user61646
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$\sqrt{2016n}$. Solve for $n$

What is the smallest natural number $n$ possible for $\sqrt{2016n}$ to be a whole integer? I can solve it by using a calculator and with trial and error but I think I have to solve it without a calculator. How would you go about the question? Thank…
DWCY
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The HCF of two numbers is $13$ and their LCM is $4095$. If one of the numbers is $819$, find the other numbers

Stuck on this question. My Workings: $$4095 = 3^2 * 5 * 7 * 13$$ $$819 = 3^2 *7 * 13$$ and I'm lost after this part. Help would be appreciated. Thank You
RTStriker
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