Question 1208363
.
Prove that given any set of $17$ integers, there exist nine of them whose sum is divisible by $2.$
~~~~~~~~~~~~~~~~~~~~~~~~~~~


As it is worded,  printed,  posted and presented,  it is  TOTALLY  and  FATALLY  wrong statement.


Take,  for example,  17 integers,  all equal to  1,  and you will  NEVER get  9  addends,
giving an even sum.   Their sum always will be  9.



Or,  if this example does not convince you,  take first 17 odd integer numbers


    1, 3, 5, 7, . . . 31, 33.


Using these numbers,  you will never get  9  of them with an even sum.



        Where did you get this gibberish ?    What is the source ?


                Just a shamefully low level of Math composing.



////////////////////////////////////



I placed this formulation in my Google browser and requested for search.


It generates first output created by Artificial Intelligence (AI).  


It becomes making some reasoning, but from its output,
it is clear that this AI incorrectly understands the problem.


The link is 


https://www.google.com/search?q=Prove+that+given+any+set+of+%2417%24+integers%2C+there+exist+nine+of+them+whose+sum+is+divisible+by+%242.%24&rlz=1C1CHBF_enUS1071US1071&oq=Prove+that+given+any+set+of+%2417%24+integers%2C+there+exist+nine+of+them+whose+sum+is+divisible+by+%242.%24&gs_lcrp=EgZjaHJvbWUyBggAEEUYOdIBCTE4MTFqMGoxNagCCLACAQ&sourceid=chrome&ie=UTF-8


On the way, this AI generates a blatant nonsense.



At the very end, it confesses that


<pre>
    Generative AI is experimental. Answers might be inaccurate or misleading. 
    Double-check for accuracy.
</pre>

It is precisely the case when this AI works INCORRECTLY.


Still is not trained to solve such problems.



Had it worked in a right way, it should/(it must) recognize that the problem is posed INCORRECTLY.