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?!

6 Responses to “Le Monde puzzle [#824]”

  1. ((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!

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

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

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