Le Monde puzzle [#824]
A rather dull puzzle this week:
Show that, for any integer y, (√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?!
A rather dull puzzle this week:
Show that, for any integer y, (√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…