TS EAMCET 9 May 2024 Shift 1 Solved Paper

To find largest positive integer K, that divides 81n+20n−1 for n∈N, we start evaluating the expression for small values of n
For n=1:811+20.1−1=100
For n=2:812+20.2−1=6600
Now,
The greatest common divisor of 100 and 6600 is 100 . Hence, K=100 is the largest integer that divides
81n+20n−1 for all n∈N
and the divisior of 100 are
1,2,4,5,10,20,25,50,100
⇒S=1+2+4+5+10+20+25+50+100=217
Hence, S−K=117