How many of the 1000 smallest positive integers are congruent to 7 modulo 29?

LiIIiam0216 Jul 2, 2024

#1**+1 **

We can write a handy equation to solve this problem.

First, let's set a variable. Let's set x as a positive integer.

Any number congruent to 7 modulo 29 can be written in the form

\(29x+7\) since it is 7 greater than a factor of 29.

thus, we can write the inequality

\(29x+7\leq 1000\)

Setting the two to equal and solving for x, we have

\(29x+7=1000\\ 29x=993\\ x \approx 34.24\)

Rounding down, we find x is 34.

So our answer is 34.

Thanks! :)

NotThatSmart Jul 2, 2024

#1**+1 **

Best Answer

We can write a handy equation to solve this problem.

First, let's set a variable. Let's set x as a positive integer.

Any number congruent to 7 modulo 29 can be written in the form

\(29x+7\) since it is 7 greater than a factor of 29.

thus, we can write the inequality

\(29x+7\leq 1000\)

Setting the two to equal and solving for x, we have

\(29x+7=1000\\ 29x=993\\ x \approx 34.24\)

Rounding down, we find x is 34.

So our answer is 34.

Thanks! :)

NotThatSmart Jul 2, 2024