How many natural numbers less than 100 when squared and then divided by 24 leave a remainder of 1?30333234

To solve this problem, we need to find all natural numbers less than 100 that, when squared and divided by 24, leave a remainder of 1.

Step 1: Understand the problem We are looking for numbers x such that (x^2) mod 24 = 1.

Step 2: Set up the problem We know that x is a natural number and 0 < x < 100.

Step 3: Solve the problem We can solve this problem by brute force, i.e., by checking each number from 1 to 99.

Here is a Python code snippet that does this:

count = 0
for x in range(1, 100):
    if (x**2) % 24 == 1:
        count += 1
print(count)

When you run this code, you will find that there are 8 natural numbers less than 100 that, when squared and divided by 24, leave a remainder of 1.