+0  
 
0
55
2
avatar

If 1,000 mod n =1, where n=1, 2, 3,4...........998, 999, 1000, just how many n are there between 1 and 1,000? Thank you for help.
 

Guest Oct 29, 2018
 #1
avatar
0

Here is a bit of computer code that calcultes this kind of question in no time.
a=1000; b=1000; c=(1); n=2; if((a % n)==1,c=(c,n),0); n++; if(n<=b,gotor-2,c);printc; c=sumfor(n, 1, b, (a % n)==1);print"Total =",c
(3, 9, 27, 37, 111, 333, 999) = 7 Numbers.

Guest Oct 30, 2018
 #2
avatar+20116 
+2

If 1,000 mod n =1, where n=1, 2, 3,4...........998, 999, 1000, just how many n are there between 1 and 1,000?

 

\(\text{Since $1000 \pmod 1 = 0$ and $1000 \pmod {1000} = 0$, $n$ can only be $2,3, \ldots , 999$.} \)

 

\(\begin{array}{|rcll|} \hline 1000 & \equiv & 1 \pmod n \\ \text{or} \\ 1000-1 &=& n\cdot m,~ \text{with } m \in \mathbb{Z} \\ 999 &=& n\cdot m,~ \text{so $n$ are all divisors of $999$ except $1$ } \\ \hline \end{array} \)

 

The divisors of 999 are:

Divisors:

1 | 3 | 9 | 27 | 37 | 111 | 333 | 999 (8 divisors)

 

n = 3 | 9 | 27 | 37 | 111 | 333 | 999 (7 numbers)

 

laugh

heureka  Oct 30, 2018

27 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.