Question 254489
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Let *[tex \Large x] represent the largest of 3 consecutive even integers.  The next lower consecutive even integer is then *[tex \Large x\,-\,2], and the next lower one is *[tex \Large x\,-\,4].  Add 'em up to get 196:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ (x\ -\ 2)\ +\ (x\ -\ 4)\ =\ 196]


Just solve for *[tex \Large x]


The problem is that the value of *[tex \Large x] that satisfies the equation is not an integer, much less an even integer.  Therefore, there is no set of three consecutive even integers such that their sum is 196.


As further proof, consider:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 62\ +\ 64\ +\ 66\ =\ 192]


Note that the sum is smaller than 196, and then next larger sum of three consecutive even integers:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 64\ +\ 66\ +\ 68\ =\ 198]


has a sum larger than 196.


Hence the statement: "The sum of three consecutive even integers is 196." is false and the largest of three non-existent integers is also non-existent.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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