Discrete MathematicsLesson 16Page1of2Discrete MathematicsLesson 16 – Strong Mathematical Inductionsimilar to induction studied beforeoestablishing truth of sequence of statements about integersobasis stepoinductive stepbasis step may contain proofs forseveralinitial valuesin inductive step, predicateP nassumed not just for one value ofn, but forallvalues throughkany statement that can be proved with“weak”induction can be proved with strong inductionTheorem 1 (Revisit from previous theorem)Any integer greater than 1 is divisible by a prime number.Proof:For the case2n, the statement is true since 2 is divisible by 2, which is a prime number.Suppose that for every integerkgreater than 1,kis divisible by a prime.If1kis prime, then it is divisible by a prime number, namely itself.If1kis not a prime, then1kabwhereaandbare integers with11akand11bk.
