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Find the smallest distinct positive numbers that provide a counterexample to show the statement is false,The sum of any two different odd numbers is divisible by 4.The counterexample is

User Qiming
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1 Answer

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22 votes

ANSWER

1 and 5

Step-by-step explanation

We want to find the two smallest distinct positive numbers that provide a counterexample for:

This means that we want to find the smallest two distinct odd numbers that make the statement false.

The statement means that:


(x+y)/(4)=n

where x and y are odd numbers and n is an integer.

The first two smallest distinct odd numbers are 1 and 3, so we have:


\begin{gathered} (1+3)/(4)=(4)/(4) \\ =1 \end{gathered}

As we can see, the sum is divisible by 4.

Let us move to the next two, 1 and 5:


(1+5)/(4)=(6)/(4)

As we can see, 6 is not divisible by 4.

This means that the smallest distinct positive numbers that provide a counterexample to show that the statement is false are 1 and 5.

User Weng
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