Question

Prove that the sum of any two integers of the form 4k+1 is even

Answer 1

Answer:

How do you prove that the sum of two consecutive integers can be written as

You don’t, because it’s not true. I wanted to write this since there are currently no less than five other answers to this question, all of them wrong.

The variable nn is almost always used to denote an integer. If we allowed nn to be any rational number, then any integer can be written as 4n+14n+1 and the statement, while true, is pointless. In all likelihood, you were asked to prove that the sum of two consecutive integers can be written as 4n+14n+1 with nn being an integer.

However, 11 and 22 are two consecutive integers, and their sum is 33. The only nn which makes 4n+1=34n+1=3 is n=12n=12, which isn’t an integer. So the sum of the two consecutive integers 1,21,2 cannot be expressed as 4n+14n+1.

The sum of two consecutive integers can always be written as 2n+12n+1, but it can be written as 4n+14n+1 only if the first integer of the two is even. If it’s odd, the sum can be expressed as 4n+34n+3, or as 4n—14n—1, but not as 4n+14n+1.

I can’t guess what the question was supposed to be. As written, what it’s asking you to prove is just not true.

Answer 2

Step-by-step explanation:

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If you 2 terms like 4k+1 ,

So after adding them you get

4k+1+4k+1=8k+2

Now Isn't 8k+2 divisible by 2 ??