Find the largest positive integer that divides every number of the form \(13^{2n}+6\), where n is a positive integer.
I just looked at the first 2.
n=1 the expression = 175
n=2 the expression = 28267
The highest common factor is 1
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).
ok, thanks Alan :)
Checked all EVEN powers of 13 up to 13^1000 + 6 and they are all multiples of 7.
+537 
+118667 
