## Le Monde puzzle [#824]

**A** rather dull puzzle this week:

Show that, for any integery, (√3-1)^{2y}+(√3+1)^{2y}is an integer multiple of a power of two.

**I** just have to apply Newton’s binomial theorem to obtain the result. What’s the point?!

an attempt at bloggin, nothing more…

**A** rather dull puzzle this week:

Show that, for any integery, (√3-1)^{2y}+(√3+1)^{2y}is an integer multiple of a power of two.

**I** just have to apply Newton’s binomial theorem to obtain the result. What’s the point?!

December 6, 2013 at 12:21 pm

((root3 – 1)^2)^y + ((root3 + 1)^2)^y = (4 – 2root3)^y + (4 + 2root3)^y which has a factor of 2^y. Still remains to show that the other factor is an integer though!

July 10, 2013 at 9:17 am

A slightly less pointless solution:

http://angrystatistician.blogspot.com/2013/07/a-slightly-less-pointless-solution-to.html

June 14, 2013 at 6:37 am

Both those terms look the same. Was one of those terms meant to have a + in it?

June 14, 2013 at 7:36 am

Thanks for spotting the typo!

June 13, 2013 at 1:25 pm

Perhaps their target audience is not exactly “professors of mathematics” ;)

June 13, 2013 at 1:29 pm

The binomial theorem is taught in (French) secondary schools…