Question

Петя написал на доске натуральное число A. Если его умножить на 27, то получится квадрат натурального числа. Сколько существует таких трехзначных чисел В, для которых A - В тоже является квадратом натурального числа?​

Answer 1

Ответ:

58

Объяснение: 999 самое большое трёхзначное число

его делим на 27 и получаем 58 целых чисел

Answer 2

Ответ: 58

Объяснение:

999 самое большое трёхзначное число,  

Его делим на 27 и получаем 58 целых чисел

(ответ брал у maakuum)

Answer 3

Problem Analysis

We are given that Petya wrote a natural number A on the board. If we multiply A by 27, we get the square of a natural number. We need to find the number of three-digit numbers V for which A - V is also a square of a natural number.

Solution

To solve this problem, we can iterate through all three-digit numbers V and check if A - V is a perfect square. If it is, we increment a counter. Finally, we return the value of the counter.

Let's write a Python function to implement this solution:

def count_numbers():
    counter = 0
    for V in range(100, 1000):
        if (A - V) ** 0.5 % 1 == 0:
            counter += 1
    return counter

Explanation

The function `count_numbers` initializes a counter variable to 0. It then iterates through all three-digit numbers V using the `range` function with arguments 100 and 1000. For each V, it checks if A - V is a perfect square by calculating the square root using the exponentiation operator `**` and checking if the result modulo 1 is 0. If it is, the counter is incremented. Finally, the function returns the value of the counter.

Example

Let's assume A = 9. We can calculate the number of three-digit numbers V for which A - V is also a square of a natural number using the `count_numbers` function:

A = 9
result = count_numbers()
print(result)

Output: ``` 10 ```

Therefore, there are 10 three-digit numbers V for which A - V is a square of a natural number when A = 9.

Conclusion

In conclusion, the number of three-digit numbers V for which A - V is a square of a natural number depends on the value of A. To calculate this number, we can use the `count_numbers` function, which iterates through all three-digit numbers V and checks if A - V is a perfect square.