SOLUTION: Find a counterexample to the statement 4^n+1 is divisible by 5. It ask me to show my work. Could you also explain what a counterexample is? Thanks for your time.
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Question 736169: Find a counterexample to the statement 4^n+1 is divisible by 5. It ask me to show my work. Could you also explain what a counterexample is? Thanks for your time.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Consider the statement: "All American made cars are painted blue." Clearly this is a false statement, and all you need to do is find one American made car that is painted some other color than blue to prove that it is a false statement. Such a car would be considered a counterexample, an example that runs counter to and disproves an assertion.
Your job is to disprove the statement: \ \left(5\ |\ 4^n\ +\ 1\right))
Read the statement thus: "For all n that are elements of the set of natural numbers, 5 evenly divides the expression 4 raised to the n power plus 1 added to the result."
One way to do this is to find some natural number 
such that when 4 is raised to the power of the selected number and 1 is added to the result that the final result is NOT divisible by 5. You only have to find one counterexample in order to disprove a statement that begins "for all". I suggest you start with 1, and then try 2...
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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