## Math Problem

For students of class 6-8 (age 12 to 14)
ataher.sams
Posts: 20
Joined: Wed Nov 30, 2011 6:24 pm
Location: Madarbari, Chittagong ,Bangladesh.

### Math Problem

Find four prime numbers less than 100 which are factor of 3$3^{32}-2^{32}$

nafistiham
Posts: 829
Joined: Mon Oct 17, 2011 3:56 pm
Location: 24.758613,90.400161
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### Re: Math Problem

$3^{32}-2^{32}$
$=(3^{16}+2^{16})(3^{16}-2^{16})$
$now,$
$=3^{16}-2^{16}$
$=(3^{8}+2^{8})(3^{8}-2^{8})$
$now,$
$3^{8}-2^{8}$
$=(3^4+2^4)(3^4-2^4)$
$=97 \cdot 65$
$=97 \cdot 5 \cdot 13$

the next thing i did isn't quite successful

$3^8+2^8$
$=17 \cdot 401$

so, the answers are
$5,97,13,17$
Last edited by nafistiham on Fri Dec 02, 2011 3:47 pm, edited 1 time in total.
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

ataher.sams
Posts: 20
Joined: Wed Nov 30, 2011 6:24 pm
Location: Madarbari, Chittagong ,Bangladesh.

### Re: Math Problem

Thnx for the answer...... Ataher Sams

nafistiham
Posts: 829
Joined: Mon Oct 17, 2011 3:56 pm
Location: 24.758613,90.400161
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### Re: Math Problem

@ataher.sams   i think you didn't notice how big mistakes i did on that post. i didn't even find out $4$ primes.now it's edited and quite fulfilled.
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

ataher.sams
Posts: 20
Joined: Wed Nov 30, 2011 6:24 pm
Location: Madarbari, Chittagong ,Bangladesh.

### Re: Math Problem I didn't see it... 'cause I was busy then.... Ataher Sams

nafistiham
Posts: 829
Joined: Mon Oct 17, 2011 3:56 pm
Location: 24.758613,90.400161
Contact:

### Re: Math Problem

could anyone post a better way to functionize
$2^8+3^8$
i just used trial and error division process
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

Labib
Posts: 411
Joined: Thu Dec 09, 2010 10:58 pm
Location: Dhaka, Bangladesh.
Contact:

### Re: Math Problem

Why don't you start a new topic on this??
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.

"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes

samiul_samin
Posts: 1004
Joined: Sat Dec 09, 2017 1:32 pm

### Re: Math Problem

ataher.sams wrote:
Wed Nov 30, 2011 6:39 pm
Find four prime numbers less than $100$ which are factors of $3^{32}-2^{32}$
This is BdMO National Junior $2008$ problem no $8$.