Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:


Math Forum » Discussions » Math Topics » alt.math.undergrad.independent

Topic: Why is 5 the answer to this question?

Advanced Search

Ara M Jamboulian

Posts: 71
Registered: 12/6/04
Re: Why is 5 the answer to this question?
Posted: Apr 21, 2013 5:34 PM

> Find the digit that appears immediately before the

Let a = 8 + sqrt(59) and b = 8 - sqrt(59)
Prove by induction that a^k + b^k is congruent to 6 mod 10 for any integer k >= 2.
Also prove that floor[a^k]=a^k + b^k - 1
It follows that floor[a^k] is congruent to 5 mod 10


[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.