+0  
 
0
57
4
avatar+531 

Find the largest positive integer that divides every number of the form \(13^{2n}+6\), where n is a positive integer.

 May 10, 2020
 #1
avatar+109519 
+1

I just looked at the first 2.  

n=1    the expression = 175

n=2    the expression = 28267

 

The highest common factor is 1

 May 10, 2020
 #2
avatar+30046 
+4

Looks like 7 is a factor of all of them (leap of faith based on the prime factorisation of ten values of n  !!):

 

(Melody, the value with n = 2 should be 28567 not 28267).

 May 10, 2020
edited by Alan  May 10, 2020
 #4
avatar+109519 
0

ok, thanks Alan :)

Melody  May 10, 2020
 #3
avatar
+1

Checked all EVEN powers of 13 up to 13^1000 + 6 and they are all multiples of 7.

 May 10, 2020
edited by Guest  May 10, 2020

18 Online Users

avatar