2. This topic mainly investigates the number theorem of divisors, because there are nine divisors, 9=3*3=(2+ 1)*(2+ 1), which shows that this three-digit number can be written in the form of a = N2 * m2 (the square of n times the square of m), and such three-digit number is:

If n=2, m can be 5,6,7,8,9, 10,1,12, 13, 14,14.

If n=3, m can be 4, 5, 6, 7, 8, 9, 10***7.

If n=4, m can take 5, 6, 7***3 numbers.

If n=5, m can be 6*** 1.

So there are1+3+7+11= 22 qualified three digits * *.

3. This question mainly examines students' application of several inferences about square numbers. For a square number, the mantissa can only be 0, 1, 4, 5, 6, 9 * * 6. We know that 358 1 is the square of 59, so the minimum value of a is 1.

4. This question mainly examines students' application of square difference formula (a2-b2)=(a+b)*(a-b), so it is 77=77* 1 or 77 =1* 7, that is, we only need to discuss A+B = 77.