A perfect square less than 500 is such that when a prime number `p_1` is subtracted or another prime number `p_2` is added to it in both cases it becomes the perfect square when `p_2 = 2+p_1`. Then `p_1+p_2` is necessarily divisible by :

Options

A. 8
B. 11
C. 4
D. all of these

Answer

To solve the problem step by step, we need to find a perfect square less than 500 that meets the conditions specified in the question.

### Step 1: Identify perfect squares less than 500
The perfect squares less than 500 are:
- \(1^2 = 1\)
- \(2^2 = 4\)
- \(3^2 = 9\)
- \(4^2 = 16\)
- \(5^2 = 25\)
- \(6^2 = 36\)
- \(7^2 = 49\)
- \(8^2 = 64\)
- \(9^2 = 81\)
- \(10^2 = 100\)
- \(11^2 = 121\)
- \(12^2 = 144\)
- \(13^2 = 169\)
- \(14^2 = 196\)
- \(15^2 = 225\)
- \(16^2 = 256\)
- \(17^2 = 289\)
- \(18^2 = 324\)
- \(19^2 = 361\)
- \(20^2 = 400\)
- \(21^2 = 441\)
- \(22^2 = 484\)