High School Mathematics Tournament | Simplification Problem✍️🖋️📘💙

[@RyanLewis-Johnson-wq6xs]

(2^101+8)/(16^13+4^14+8)=562949919866881=2^49-2^25+1 It’s in my head.

[@januswang]

= 2^3(2^98 + 1)/2^3(2^49 +2^25 + 1) = (2^98 + 1) / (2^49 + 2^25 + 1) = (2^49 + 1)^2 - 2*2^49) / ((2^49 + 1) + 2^25) = ((2^49 + 1)^2 - 2^50) / ((2^49 + 1) + 2^25) = (2^49 + 1) - 2^25 = 2^49 - 2^25 + 1

[@davidseed2939]

(4a⁴+1)/(2a²+2a+1) where a=2²⁴ multiply top and bottom by (2a²-2a+1) = (4a⁴+1) (2a²-2a+1)/( (2a²+2a+1) (2a²-2a+1) = 2a²-2a+1 2^29 -2^25+1= 503316481

[@ajabkhan9320]

It can further be simplified.

[@SantiGio2005]

Which if we solve, the result in only one number is 562,949,919,866,881