# Question #eb541

##### 3 Answers

See below.

#### Explanation:

If

Making now

Now solving for

for

we get the

The only such integers are

#### Explanation:

Consider the fact that the perfect squares are generated by successive addition of the odd integers.

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We have been asked to find all pairs of perfect squares whose difference is

A bit of algebra will show that if the sum of **two consecutive odds** is

This makes the squares

The middle number is

There are no **four consecutive odd** integers that sum to 36.

The first **six consecutive odds** sum to

This gives us the other solution of

The middle number is

It is not possible to find **eight or more consecutive odds** that sum to

And another solutions.

#### Explanation:

Then

Therefore,

the integer factorizations of

Because

By exhaustion, the only two possibilities are

**first**

**second**