<PRE><B>Question 736169</B>
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Consider the statement:  &quot;All American made cars are painted blue.&quot;  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:  *[tex \LARGE \left(\forall\ n\ \in\ \mathbb{N}\right)\ \left(5\ |\ 4^n\ +\ 1\right)]


Read the statement thus:  &quot;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.&quot;


One way to do this is to find some natural number *[tex \LARGE n] 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 &quot;for all&quot;.  I suggest you start with 1, and then try 2...


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
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My calculator said it, I believe it, that settles it
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