+287 How many of the 1000 smallest positive integers are congruent to 1 modulo 9? Can you also explain what a modulo is?
+963 Modulo is essentially the remainder we get when we divide two numbers.
For example, we have
\(10 \equiv 1 (\mod 3)\)
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
\(9n+1 \equiv 1 (\mod 9)\)
We simply can write the equation
\(9n+1 \leq 1000\)
Now, we simplfy solve for n. Setting the two equations togther, we have
\(9n = 999\\ n=111\)
Thus, our answer is 111.
Thanks! :)
