## Maths challenge 15

Posted by Chris on September 25, 2011 – 7:55 am

Prove that for integer n > 2, that 3^n-1 doesn’t divide 5^n-1 exactly.

You’ll find http://trickofmind.com/?p=957#comments useful.

Posted by Chris on September 25, 2011 – 7:55 am

Prove that for integer n > 2, that 3^n-1 doesn’t divide 5^n-1 exactly.

You’ll find http://trickofmind.com/?p=957#comments useful.

September 26th, 2011 at 7:13 pm

not sure how to officially prove it with a geometric proof or something, but 3 multiplied by itself any number of times will never produce a number with a 0 or 5 in the ones digit, and 5 multiplied by itself any number of times will always produce a number with a 0 or 5 in the ones digit

September 27th, 2011 at 5:26 am

Hi leadfarmer5. Right now I wish that it was as simple as that. I may have bitten off more than I can chew.

I’ve number crunched up to n = 910 000 (I’ve now stopped checking), so far, only n = 1 or 2 gives an exact division. i.e.

(5

^{1}-1)/(3^{1}-1) = 4/2 = 2(5

^{2}-1)/(3^{2}-1) = 24/8 = 3