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

 Jul 22, 2020
 #1
avatar+30947 
-2

See https://web2.0calc.com/questions/i-still-need-help_1#r3

 Jul 22, 2020
 #2
avatar+248 
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umm...that doesn't really help

 Jul 22, 2020
 #3
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What do mean "that doesn't help"? You got 2 correct answers there! if you don't undestand them, that is YOUR problem !!!.

 Jul 22, 2020
 #4
avatar+1130 
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I think it's 19

 Jul 22, 2020
 #5
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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
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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
 #8
avatar+1130 
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I had a different explanation

jimkey17  Jul 22, 2020
edited by jimkey17  Jul 22, 2020
 #9
avatar+1130 
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Guest, if you still don't believe me then here's what i'll say:

 

 

 

some people have the same answers but different explantions

jimkey17  Jul 22, 2020
 #10
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You must be joking if you think your "solution" has better explanatory power than Alan's solutions. Alan Uses RIGOROUS mathematical solution, using exponents and difference of two squares, to arrive easily and elegantly at the correct answer. Please don't compare the two!.

Guest Jul 22, 2020
 #6
avatar+248 
+1

I just don't get what the link 

See https://web2.0calc.com/questions/i-still-need-help_1#r3

does, thats all

 Jul 22, 2020

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