Amazing number 73

73 x 14 = 1022. From the product find the sum of square of last two digits and sqaure of remaining digits.
10^2 + 22^2 = 584 = 73 x 8. Repeat the above for the product 584
5^2 + 84^2 = 7081 = 73 x 97. Repeat the above for the product 7081
70^2 + 81^2 = 11461 = 73 x 157 . Repeat the above for product
114^2 + 61^2 = 16717 = 73 x 229 and so on...
167^2 + 17^2 = 28178 = 73 x 386
281^2 + 78^2 = 85045 = 73 x 1165
850^2 + 45^2 = 724525 = 73 x 9925 and so on......
So all sums will have 73 as one of the factor. Amazing is it not! But then why this happens?
Can we prove it? (Another one of 73 is 73 x 137 = 10001; 100^2 + 01^2 = 10001 = 73 x 137)