Processing math: 100%
 
+0  
 
0
36
1
avatar+363 

How many of the 1000 smallest positive integers are congruent to 1 modulo 9? Can you also explain what a modulo is?

 Jul 1, 2024
 #1
avatar+1952 
+1

Modulo is essentially the remainder we get when we divide two numbers.

For example, we have

101(mod3)

 

In this case, 1 is the remainder, 3 is the number we divide into 10. 

Thus, we say that 10 is congruent to 1 modulo 3. 

 

To solve the problem, we have the equation

9n+11(mod9)

 

We simply can write the equation

9n+11000

 

Now, we simplfy solve for n. Setting the two equations togther, we have

9n=999n=111

 

Thus, our answer is 111. 

 

Thanks! :)

 Jul 1, 2024

0 Online Users