How many of the 1000 smallest positive integers are congruent to 1 modulo 9? Can you also explain what a modulo is?
Modulo is essentially the remainder we get when we divide two numbers.
For example, we have
10≡1(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+1≡1(mod9)
We simply can write the equation
9n+1≤1000
Now, we simplfy solve for n. Setting the two equations togther, we have
9n=999n=111
Thus, our answer is 111.
Thanks! :)