Question 120479: Find a counterexample to show that the following statement is incorrect:
“The sum of any two odd numbers is divisible by 4”
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887)   (Show Source):
Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website! show that the following statement is  :
“           ."
first recall some of  relating to  numbers:
-All odd numbers can be expressed as  where  is a whole number.
-Sum or difference of  numbers is   .
-Sum of and  number is  .
also recall that:
-A number  by , when the number formed by the last two right hand digit is divisible by .
-Or, a number is  by , if its two last digits are  or they make a   , which is divisible by .
Any integer can be put into  of the four cases  ,  ,  , and  .
Since and are , only the cases and need be considered.
 that  is the  number. Then  has a factor of  and  has a factor of  ; that is, is divisible by .
If we choose  numbers, let’s say  and  , and  their squares ( in this case) we will find that the  is  by .
 …. …… => .. by .
If and  are  they have the form  and  .
Then  , which has a  of when divided by and so can not be equal to , which is exactly divisible by .
Therefore the  that is is  .
Since   that  of the terms   , one of  and , and   .
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