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## #1 2005-05-20 15:29:00

cheer99
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### Puzzling Puzzle

Hi All-

I need some help. I'm so bad at math.

Here is the questions:

what is the number of prime numbers between one and a million that become a perfect square if you add 1 to them?

Thanks a bunch!
Delina

## #2 2005-05-20 15:57:40

MathsIsFun

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### Re: Puzzling Puzzle

You must be good at math to be even attempting that one!

By "perfect square" I will assume that you mean the squares of the whole numbers 1,2,3,4 ... which are 1,4,9,16 ... etc

So, to start with, you are dealing with 1000 candidate numbers, because 1000^2 = 1,000,000 and your question said that is as far as you need go.

You could use a spreadsheet to generate those 1,000 numbers, subtract 1 in the next column and compare that to a list of primes. That would give you your answer.

There may be a way of cutting the problem down a little bit by using the properties of primes or perfect squares ...

Let me see, a perfect square is n^2 and you are asked to see if that is prime when you subtract one, or:

Is n^2-1 a prime (for n=1,2,3,...1000)

Now, a simple property of primes is that they are odd numbers (except for 2), so that would mean that the perfect squares must be even (because you subtract one). So that eliminates half of the perfect squares right there (even times even is even, odd times odd is odd)

So, we are now trying to check the squares of 2,4,8, ... 1000

For example:

2*2 = 4, -1 = 3, is 3 prime? YES
4*4 = 16, -1 = 15, is 15 prime? NO
6*6 = 36, -1 = 35, is 35 prime? NO

Only 497 more numbers to check.

Now, I have a suspicion that there are no more "YES" answers ... because the factors work out neatly as:

2*2 = 4, -1=3 ==> has factors 1 and 3
4*4 = 16, -1=15  ==> has factors 3 and 5
6*6 = 36, -1=35 ==> has factors 5 and 7
8*8 = 64, -1=63 ==> has factors 7 and 9
10*10 = 100, -1=99 ==> has factors 9 and 11

There is a pattern!

And the pattern is this:

n^2 = (n-1)(n+1) + 1

(because (n-1)(n+1) = n^2 +n - n - 1 = n^2 - 1)

So that means NONE of them will be prime (except for 2*2-1=3), as they have factors when you subtract one !!

A lovely trick question, thanks.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

## #3 2005-05-21 00:56:23

cheer99
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### Re: Puzzling Puzzle

thanks for the helps, but in your post you put subtract, but in my question it says add one. So is your post correct to help me?

Thanks again for the help!

## #4 2005-05-21 08:23:00

MathsIsFun

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### Re: Puzzling Puzzle

"prime numbers ... that become a perfect square if you add 1 "

I just turned it around to be

"perfect squares ... that become a prime number if you subtract 1 "

Yep, I believe there are just 1. But that's just me. I do get things wrong.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

## #5 2005-05-21 20:03:51

Roraborealis
Super Member

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### Re: Puzzling Puzzle

Ah, so do us all.

School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

## #6 2005-05-21 23:43:30

Zach
Super Member

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### Re: Puzzling Puzzle

I don't.

Boy let me tell you what:
I bet you didn't know it, but I'm a fiddle player too.
And if you'd care to take a dare, I'll make a bet with you.

## #7 2005-05-21 23:57:36

cheer99
Novice

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### Re: Puzzling Puzzle

Thanks a bunch! I really appreciate it. We get an extra 10 points on the final exam if we get it right! College Math is so much harder then high school math!

## #8 2005-05-21 23:58:43

Zach
Super Member

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### Re: Puzzling Puzzle

That's probably the idea of it being a higher level math.

Boy let me tell you what:
I bet you didn't know it, but I'm a fiddle player too.
And if you'd care to take a dare, I'll make a bet with you.

## #9 2005-05-22 08:44:41

MathsIsFun

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### Re: Puzzling Puzzle

Har-de-har ...

'Tis true though, at a certain level math goes into overdrive.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

## #10 2005-05-22 19:01:07

Zach
Super Member

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### Re: Puzzling Puzzle

Foolish maths. Always trying to be clever.

Boy let me tell you what:
I bet you didn't know it, but I'm a fiddle player too.
And if you'd care to take a dare, I'll make a bet with you.

## #11 2005-05-22 22:17:42

Roraborealis
Super Member

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### Re: Puzzling Puzzle

Isn't that the point of school?

School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

## #12 2005-05-22 22:30:18

Vulcan
Full Member

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### Re: Puzzling Puzzle

um............
no?
or.............
yes?
wait..........
i know this one...........................................................................
um....................
i think................
yes?

one day, i couldn't find my hat
then it occured to me that i didn't have one
so i didn't where it!!!

## #13 2005-05-22 22:30:58

Roraborealis
Super Member

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### Re: Puzzling Puzzle

Correct.

School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

## #14 2005-05-22 22:33:30

Vulcan
Full Member

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### Re: Puzzling Puzzle

wahoooooooooooooooooooooo!!!!!!!!!!!!!11
i am the smartest kid in the universe!
or........
atleast the mathsisfunniverse!

one day, i couldn't find my hat
then it occured to me that i didn't have one
so i didn't where it!!!

## #15 2005-05-22 22:49:18

Roraborealis
Super Member

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### Re: Puzzling Puzzle

If you say so.........

School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

## #16 2005-05-23 02:23:51

Zach
Super Member

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### Re: Puzzling Puzzle

Riiiiiight.

Boy let me tell you what:
I bet you didn't know it, but I'm a fiddle player too.
And if you'd care to take a dare, I'll make a bet with you.

## #17 2005-05-23 18:09:26

insomnia
Real Member

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### Re: Puzzling Puzzle

Yes, ok. If you want to believe that fine with us. Who are we to destroy your fragile pysche.

Friends are angels who lift our feet when our own wings have trouble remembering how to fly

## #18 2005-05-23 21:39:06

ppl
Novice

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### Re: Puzzling Puzzle

Help me im stuck on the gcse topic and i really want to be a gr8 mathmatician. its so hard for me because im have a huge reputation as a i math brain but i just can do divison plzzzzzzz help me!!!!!!!!!!!!

## #19 2005-05-23 21:40:07

ppl
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### Re: Puzzling Puzzle

#### ppl wrote:

Help me im stuck on the gcse topic and i really want to be a gr8 mathmatician. its so hard for me because im have a huge reputation as a i math brain but i just can do divison plzzzzzzz help me!!!!!!!!!!!!

sorry i ment CANT and i aint no novice im goin to recive the highest award in my maths class a ************8 see beat ne if u can moo ha ha ha

## #20 2005-05-23 21:41:09

ppl
Novice

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### Re: Puzzling Puzzle

#### ppl wrote:

Help me im stuck on the gcse topic and i really want to be a gr8 mathmatician. its so hard for me because im have a huge reputation as a i math brain but i just can do divison plzzzzzzz help me!!!!!!!!!!!!

sorry i ment CANT and i aint no novice im goin to recive the highest award in my maths class a ************8 see beat ne if u can moo ha ha ha

fine then dont help me u r all evil...... i just goin to go in my corner and cry!! sob sob sniff

## #21 2005-05-23 22:50:18

MathsIsFun

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### Re: Puzzling Puzzle

Hello "ppl"

There was only 2 minutes between your first and last post ... this is a forum,  not a phone conversation

When you post a question here you need to give people a chance to come on the forum, read your message and reply. This can be many hours to days sometimes, but we will do the best we can to help.

So, can you tell us what your problem is with division - is it long division?

Have you tried reading our pages on it starting here

And you can practice with these worksheets - there are normal division and long division worksheets, and you can view them with or without answers.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Guest

neopets?

## #23 2005-05-25 16:30:31

MathsIsFun

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### Re: Puzzling Puzzle

Like this? No, sorry.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

## #24 2005-05-26 07:03:02

Ellie
Guest

### Re: Puzzling Puzzle

#### cheer99 wrote:

Thanks a bunch! I really appreciate it. We get an extra 10 points on the final exam if we get it right! College Math is so much harder then high school math!

lol! More like your trying to get the ansewer for this weeks Lenny Conundrem on neopets.com!

## #25 2005-05-26 07:41:42

MathsIsFun

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### Re: Puzzling Puzzle

Is that right? LOL !!

Do I get a prize for answering it, then?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman