pathfinder

Forgot your password?

Forgot your username?

New user register here

Doubts of Number Theory Sheet 2

In this forum, please discuss the questions appearing in the QA class sheets :especially the practice and the DS questions at the end of the sheet.

Doubts of Number Theory Sheet 2

Postby sadmin » Tue Feb 26, 2013 9:48 am

Dear All,

Pleas post your doubts of number theory sheet 3 on this thread.
sadmin
Site Admin
 
Posts: 212
Joined: Wed Feb 13, 2013 5:51 am

Re: Doubts of Number Theory Sheet 2

Postby sadmin » Thu Feb 28, 2013 12:36 pm

Q23

301 = 7*43,

so 300 ≡ -1 (mod 7)

Then 300^3000 - 1 ≡ (-1)^3000 - 1 ≡ 1 - 1 ≡ 0 (mod 7)

So 7 divides 300^3000 - 1

297 = 27*11,

so 300 ≡ 3 (mod 11)

Then,
300^3000 - 1 ≡ 3^3000 - 1 ≡ (3^5)^600 - 1 (mod 11)

But 3^5 = 243 = 22*11 + 1
so 3^5 ≡ 1 (mod 11)

Then
300^3000 - 1 ≡ (3^5)^600 - 1 ≡ 1^600 - 1 ≡ 0 (mod 11)

So 11 divides 300^3000 - 1

Finally, 299 = 23*13,

so 300 ≡ 1 (mod 13)

Then
300^3000 - 1 ≡ 1^3000 - 1 ≡ 0 (mod 13)

So 13 divides 300^3000 - 1

Since 7, 11, 13 are all prime, it follows that their product, 1001 divides 300^3000 - 1
sadmin
Site Admin
 
Posts: 212
Joined: Wed Feb 13, 2013 5:51 am

Re: Doubts of Number Theory Sheet 2

Postby sadmin » Thu Feb 28, 2013 12:37 pm

You are right - for both these questions it is better to approach from the options.
sadmin
Site Admin
 
Posts: 212
Joined: Wed Feb 13, 2013 5:51 am

Re: Doubts of Number Theory Sheet 2

Postby gaurav1399 » Thu Feb 28, 2013 12:40 pm

Kindly solve question number 16 and 23 in the practice questions. Are we to proceed by options in both the questions or is there a shorter way out?
gaurav1399
 
Posts: 48
Joined: Wed Feb 27, 2013 7:49 am


Return to QA - Class Sheets -Phase 1

Who is online

Users browsing this forum: No registered users and 1 guest

cron