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Is it, or is it not? (Posted on 2007-04-10) Difficulty: 4 of 5
Is (258+1)/5 an integer? A prime?

See The Solution Submitted by Federico Kereki    
Rating: 3.6667 (3 votes)

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Solution Just a simple pattern | Comment 5 of 12 |

X=(2^58+1)/5

if X is divisible by 5 then last digit must end with 0,5

for this 2^58 must end with 4 or 9,9 not possible

2^2=4

2^6=64

2^10=1024

2^14=16384

......


So got the catch,removing first 2 from 58 we are left with 56 & it 

is divisible by 4,so we conclude X IS AN INTEGER.

Now catch this pattern


(2^6+1)/5=13(prime)
(2^14+1)/5=(prime)
(2^22+1)/5=(prime)
(2^30+1)/5=(prime)
......
leaving 2 we have 56 & it is also divisible by 8,but our pattern passes through 54 not through 58 so we conclude X IS NOT A PRIME

  Posted by Nishant on 2007-04-10 15:52:41
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