What is this saying??!!!?

Question

Ok so what does this phrase mean? "Every odd whole number can be written as the difference of two squares." And is this a true statement or a false one. If it is false explain to me why, but explain it as if u were talking to a 5th grader....Yeah I'm that bad at math.....

Answer 1

Some of the whole numbers are,1, 2, 3, 4, 5, 6, etc....

That makes every ODD whole number to be 1, 3, 5, 7... as they are odd numbers.

Squares are 1*1, 2*2, 3*3.... otherwise expressed as 1^2, 2^2, 3^2....

So it is saying, every number such as 1, 3, 5, 7 can be expressed as some number squared MINUS another number squared.

You can prove this is FALSE by coming up with ONE example that does not fit this rule. Proving this to be TRUE will require some work.

Start from 1... how can you have a number squared minus another number squared equal to 1? Then move to 3...., then to 5....

I'll do just a few for you.

0 = 1^2 - 0^2
3 = 2^2 - 1^2
5 = 3^2 - 2^2

See developing a pattern? Can you generalize this and come to a conclusion? (although this is not a formal proof)

Answer 2

It n is odd, n = 2m + 1, say, then
n = 2m + 1 = a^2 - b^2
for some integer a and b.

this is true.. Here's how you prove it:
the odd number n = 2m+1 = (m+1)^2 - m^2, the difference of two consecutive squares

Here are some examples
3 = 4 - 2
5 = 9 - 4
7 = 16 - 9
9 = 25 -16
11 = 36 -25
13 = 49 -36
15 = 64 - 49
17 = 81 - 64
19 = 100 - 81
21 = 121 - 100
23 = 144 - 121

Answer 3

It is a true statement for any odd whole number (integer) greater than one. See the web site cited.

Here is how to find two squares whose difference is the selected odd number:

Subtract one from the odd whole number.

Divide the result by two to get the FIRST number you will square.

Add one to the FIRST number to get the SECOND number you will square.

Check this by subtracting the square of the FIRST (smaller) number from the square of the SECOND (larger) number.

Example:

Find two squares whose difference is equal to 311.

311 -1 = 310

310 / 2 = 155 (first number to be squared)

155 + 1 = 156 (second number to be squared)

Subtract square of first number from square of second number:

(156)^2 - (155)^2 = 24,336 - 24,025 = 311

Now, why does this work? Go read the article.

Answer 4

I don't know ask some one else