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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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How can I determine the relationship between some variables in an expression so that the final result is always a natural number?

In a current project that I am working on, I have to determine relationship between various variables so that the final result I get by solving the equation is a natural number. For example, one such equation is $$\frac{(D_2*B_2 - D_1*B_1)}{(D_1*M_1…
iKnowNothing
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Is 3/2 undefined when only considering the natural numbers?

If we only consider the natural numbers, is 3/2 undefined? If not what is the answer?
ArturPhilibin
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Distance between point p and origin

How to prove that the distance between the origin and the point $P$ is a natural number, where $P=(n, n+1, n(n+1))$.
jofernando
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Find all functions $f:\mathbb{N} \rightarrow \mathbb{N}$ that satisfy $2f(m+n) = f(m)f(n)+1$ for all $m,n \in \mathbb{N}$

Problem: Find all functions $f:\mathbb{N} \rightarrow \mathbb{N}$ that satisfy $2f(m+n) = f(m)f(n)+1$ for all $m,n \in \mathbb{N}$
Edward Sakamoto
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