Without using a calculator, find the largest prime divisor of \(5^{12}- 2\cdot 10^6 +2^{12} \).

imdumb Jul 22, 2020

#3**0 **

What do mean "that doesn't help"? You got 2 correct answers there! if you don't undestand them, that is YOUR problem !!!.

Guest Jul 22, 2020

#4

#5**+2 **

since we have that 2*10^6=2000000 and 5^12=244140625 and 2^12=4096 so the equation becomes 244140625-2000000+4096=(244140625-2000000)+4096=242140625+4096=242144721 where we know 19 is one of the factors since we have 3 x 3 x 3 x 3 x 7 x 7 x 13 x 13 x 19 x 19 = 242,144,721. It can also be written in exponential form as 3^4*7^2*13^2*19^2.

jimkey17
Jul 22, 2020

#7**-1 **

Jimkey17: What is the "solution" given by Alan and one by another Guest? Isn't it 19? What did you do that is different from their answers?

Guest Jul 22, 2020