Square of 101, 102, 103, ..., 1001, 1002, ..., ...

Consider the following squares:

101 * 101 = 10201
102 * 102 = 10404
103 * 103 = 10609
104 * 104 = 10816
...
109 * 109 = 11881

In all of the above squares, there is a simple pattern as described in the following.

101 * 101 = <-- five digits
10201
10201 <-- this bold '1' is calculated as 1*1 (101 * 101)
10201 <-- this bold '2' is calculated as 1+1 (101 * 101)
10201 <-- this bold '1' is due to 100*100=10000 (five digits)

Let's see for 102:

102 * 102 = <-- five digits
10404
10404 <-- this bold '4' is calculated as 2*2 (102 * 102)
10404 <-- this bold '4' is calculated as 2+2 (102 * 102)
10201 <-- again, this bold '1' is due to 100*100=10000 (five digits)

Now, let's see for 103:

103 * 103 = <-- five digits
10609
10609 <-- this bold '9' is calculated as 3*3 (103 * 103)
10609 <-- this bold '6' is calculated as 3+3 (103 * 103)
10609 <-- again, this bold '1' is due to 100*100=10000 (five digits)

Now, for 109:

109 * 109 = <-- five digits
11881
11881 <-- this bold '81' is calculated as 9*9 (109 * 109)
11881 <-- this bold '18' is calculated as 9+9 (109 * 109)
11881 <-- again, this bold '1' is due to 100*100=10000 (five digits)

This pattern can also be seen in 110, 111, ...

Now, consider the following squares:

1001 * 1001 = 1002001
1002 * 1002 = 1004004
1003 * 1003 = 1006009
1004 * 1004 = 1008016
...
1009 * 1009 = 1018081

It must be easy for you to extract the pattern!

Now try:

10000001 * 10000001
10000002 * 10000002
10000009 * 10000009
100000001 * 100000001
100000002 * 100000002
100000009 * 100000009