SOLUTION: Find a counterexample to show that the following statement is incorrect: “The sum of any two odd numbers is divisible by 4”

Algebra.Com
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): You can put this solution on YOUR website!
3+7=10 which is not divisible by 4
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Cheers,
Stan H.

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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