Integer Parities Even, Yes Even!

Number Theory Level 2

If $x$ , $y$ and $z$ are distinct positive integers, can $x + y$ , $y + z$ and $x + z$ be distinct even Fibonacci numbers ?

This is the fun twist of the first and second weekly problems.

Yes, there are some triplets that work. No, never.

1 solution

Skye Rzym
Aug 9, 2017

If $x$ , $y$ , and $z$ are positive integers, then we can make a triangle with sides $x+y$ , $y+z$ , and $z+x$ . But, we can't make a triangle with distincts Fibbonacci's number as its sides, especially for distincts even Fibbonacci's number. So, that's impossible.

Integer Parities Even, Yes Even!

1 solution

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