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Re: Why is 5 the answer to this question?
Posted:
Apr 21, 2013 5:34 PM


> > > Find the digit that appears immediately before the > decimal point in: (8 + sq root(59))^(2013!)? > > Idea: 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



