令sqrt( a^2 - 11664 ) = b
=> a^2 -11664 = b^2
=> ( a + b )( a - b ) = 11664
因式分解:
11664 = 2^4 * 3^6 = 108^2
a + b , a - b 必為偶數 且 a > b
所以 a - b 可能的值為:2 , 4 , 6 , 8 , 12 , 18 , 24 , 36 , 54 , 72 ( a - b < 108 )
a - b = 2 => a = ( 5832 + 2 ) / 2 = 2917
a - b = 4 => a = ( 2916 + 4 ) / 2 = 1460
....
故 a 所有可能值之和為[ ( 5832 + 2 ) + ( 2916 + 4 ) + ( 1944 + 6 ) + ( 1458 + 8 ) + ( 972 + 12 ) + ( 648 + 18 ) + ( 486 + 24 ) + ( 324 + 36 ) + ( 216 + 54 ) + ( 162 + 72 ) ] / 2 = 7597#
也就是 11664 因式分解後所有因數之和 ( 扣除 108 )