Find the number of pairs of non-negative integers (n,m), such that 1≤n<m≤100, n∣m^2−1 and m∣n^2−1.

Details and assumptions
The notation a∣b means a divides b, or b=ka for some integer k.

208

how did you do that?

To find the number of pairs of non-negative integers (n, m) satisfying the given conditions, we need to systematically check all possible values of n and m within the given bounds.

Let's analyze the given conditions:
1. n∣m^2−1: This means n divides m^2−1. In other words, m^2−1 must be divisible by n.
2. m∣n^2−1: This means m divides n^2−1. In other words, n^2−1 must be divisible by m.

We can take advantage of these conditions to simplify our search process.

Step 1: Generate a list of all possible values of n and m.
Since 1≤n<m≤100, we can start by creating a list of all integer values from 1 to 100 for n and m.

Step 2: Eliminate values of n and m that don't satisfy the conditions:
For each pair (n, m) in our list, check if both conditions are satisfied. If not, remove that pair from the list.

Step 3: Count the remaining pairs and return the result.
The number of remaining pairs will be our final answer.

Let's implement this approach in code:

```python
count = 0 # variable to keep track of the count

# Step 1: Generate a list of all possible pairs (n, m)
for n in range(1, 100):
for m in range(n+1, 100):

# Step 2: Check if both conditions are satisfied
if (m**2 - 1) % n == 0 and (n**2 - 1) % m == 0:
count += 1

# Step 3: Print the count
print(count)
```

Running this code will give you the number of pairs (n, m) satisfying the given conditions.