Posted on: Fri, 2008-02-01 14:43
Reminder Practice Qs – Fermat’s Little Theorem
I have posted a topic on Fermat’s little theorem @ http://www.cat4mba.com/node/6104
Few questions relevant to the above topic
Q1. What is the reminder when 1139 is divided by 19
Q2. Find the reminder when 591 is divided by 91
Q3. Find the following reminders
a. 757575is divided by 37
b. 2100 is divided by 101
c. 20 51 97 is divided by 17
Q2. Find the reminder when 591 is divided by 91
Q3. Find the following reminders
a. 757575is divided by 37
b. 2100 is divided by 101
c. 20 51 97 is divided by 17
__________________
n/a
n/a
|
|
 |
Q3a. 75 = 37 (mod 1)
So 75 75 75 divided by 37 'll give reminder 1.
Q3b. 2100 is divided by 101
reminder 1
n/a
n/a
Q1. What is the reminder when 1139 is divided by 19
11 and 19 is prime to each other so 11^36/19=1 reminder so final reminder=11*11*11/19=1 reminder
Little Star
n/a
Q2. Find the reminder when 591 is divided by 91
91 and 5 prime to each other so 5^90/91=1 reminder so reminder =5
Little Star
n/a
This comment has been moved here.
Hi..
Can you please explain the above soluution?
how the step 11^36/19 comes?
thanks
hi
here is the solution
Q) rem when 11^39 divided by 19
here since 11 and 19 are co prime so according to euler theorem e(19)=18
so acc to euler 11^18*11^18*11^18 (i.e. 11^36) /19 rem=1
so rest is 11^3/19 so rem is 1
thanks a lot..:-)
i guess i need lot more practise in apt....
Solution to Q1....
11^39/19
=> (11^3)^13 /19
=> (1331)^13 /19
=> (1330 + 1)^13/19
=> as 1330 is divisible by 19, every factor of the expansion will contain a 1330...
except
(1)^13/19
therefore: remainder is 1.
Hope you get it now.
Post new comment