Prove that an integer is odd if and only if it is the sum of two consecutive integers.

A proof can be as follows:

Step-by-step explanation:

Remember that an odd interger is of the form where is a integer and remember that two consecutive integer are two numbers of the form

Suppose the is an odd integer.

Then must be an even integer and hence divisible by 2. Then we define

Then we have that

The converse is as follows:

Let an integer, then  are two consecutive integers. Then

is an odd integer.

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step-by-step explanation:

i = 2 / - 5

step-by-step explanation:

evaluation of ( 2 - 4 ) ( p + q ) when p = 2 and q = 5 i, by putting values of p and q,