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MATHEMATICAL INDUCTION MATHEMATICAL INDUCTION Math Links PDF format Naoki Sato's Solutions PDF Spanish Version connected with Number Theory.Some properties may be proved in different ways.For more exercises, problems, puzzles, games, math riddles, brain teasers, etc. to see Math Links (not only of math induction). PROBLEM 1 Let : F(n)= p-1 k=1 k n(p-1)+1 -n(n-1) p-1 k=1 ((k )/2) - p(p-1)(n(p-1)+1)/2 Prove by induction that F(n) is divisible by p , for all integers n Hint PROBLEM 2 Use mathematical induction to prove the following: FIB(n) (FIB(n+2)=FIB(n+1)+FIB(n); FIB(1)=1,FIB(2)=1. Fibonacci sequence) Hint PROBLEM 3 Prove the following in more ways than one : n+1 FIB(n) (FIB(n+2)=FIB(n+1)+FIB(n); FIB(1)=1,FIB(2)=1. Fibonacci sequence ) Hint PROBLEM 4 We guess that: S M i=1 a i and that; S M i=1 a i kbc are divisible by b c i are relatively prime with respect to b and c). Let : F(n)= M i=1 a i 1+(b-1)(c-1)n Prove by induction that : F(n) is divisible by b c ,for all integers n Solution PROBLEM 5 Let a, b, c be three positive integers where c= a + b . Let p be an odd factor of a +b +c (a +b +c ) is divisible by p.

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