Question 1170387
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I'm assuming that you mean the quotient and remainder are equal otherwise your question doesn't make sense.  The question is very poorly worded, however.  You should also define "Natural Number" since it could mean either the positive integers or the non-negative integers.  I will assume the former.


If a natural number *[tex \Large n] divided by another natural number *[tex \Large d] has a quotient *[tex \Large q] and remainder *[tex \Large r], then the following relation must hold:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ dq\ +\ r\ =\ n]


But if *[tex \Large q] and *[tex \Large r] are equal, then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ dr\ +\ r\ =\ n\ \Right\ (d\,+\,1)r\ =\ n]


For your problem, *[tex \Large d\ =\ 7]


So *[tex \LARGE \ \ \ \ \ \ \ \ \ \ 7q\,+\,r\,=\,n\,&\,q\,=\,r\,\Leftrightarrow\,8r\,=\,n\,\forall\,r\,\in\,\mathbb{N}]


																
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
*[illustration darwinfish.jpg]

From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> 
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