Let -LSB- math -RSB- S _ -LCB- n -RCB- = n ^ -LCB- 2 -RCB- + 20n + 12 -LSB- / math -RSB- , where -LSB- math -RSB- n -LSB- / math -RSB- is a positive integer . What is the sum of all possible values of n for which -LSB- math -RSB- S _ -LCB- n -RCB- -LSB- / math -RSB- is a perfect square ?
Given -LSB- math -RSB- S_n = n ^ 2 +20 n + 12 -LSB- / math -RSB- . What will be the sum of positive integers such that -LSB- math -RSB- S_n -LSB- / math -RSB- will be a perfect square ?