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Without using a calculator, find the largest prime divisor of 5^12 minus 2 times 10^6 plus 2^12.

 Jul 14, 2020
 #1
avatar
+2

625  x   625  x  625 =244,140,625

 

244,140,625  - [2 x 1,000,000] =242,140,625

 

2^4  x  2^4  x  2^4 =16  x  16  x 16 =4,096

 

242,140,625  +  4,096 =242,144,721

 

242,144,721  = 7 x 7 x 9 x 9 x 13 x 13 x 19 x 19

 

The largest prime divisor = 19

 Jul 15, 2020
 #2
avatar+254 
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Thanks........ but I don't think that's correct. 

 Jul 15, 2020
 #3
avatar+30926 
+2

Why don't you think that's correct?

 

Here's another way of doing it:

 

Clearly, 19 is the largest prime factor.

Alan  Jul 15, 2020
 #4
avatar+254 
+1

Ohhh that makes more sense!

I thought it was a bit low...

Tysm!!!

HelpBot  Jul 15, 2020
 #5
avatar+110715 
-1

Next time please add the explanation of why you think whatever you think. 

(I mean right from the beginning)

People like feedback.

If you think an answer is not right, or you have doubts, you should explain what those doubts are.

Melody  Jul 17, 2020
edited by Melody  Jul 17, 2020
 #6
avatar+110715 
-1

Thanks guest and Alan for your explanations   laugh

Melody  Jul 17, 2020
 #7
avatar+254 
0

Okay, thanks!

HelpBot  Jul 17, 2020

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