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“For every nonnegative integer n, (8n – 3n) is a multiple of 5.” (That is, “For...

“For every nonnegative integer n, (8n – 3n) is a multiple of 5.”

(That is, “For every n≥0, (8n – 3n) = 5m, for some m∈Z.” )

  1. State what must be proved in the basis step.    

  2. Prove the basis step.    

  3. State the conditional expression that must be proven in the inductive step.  

  4. State what is assumed true in the inductive hypothesis.

  5. For this problem, you do not have to complete the inductive step proof. However, assuming the inductive step proof can be completed, state the final conclusion of this proof by mathematical induction.

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