Remainder when 7^103 is divided by 24 , Mathematics

Assignment Help:

 Find the remainder when 7^103 is divided by 24

Solution) we know by the concept of mod that.....

  49 is congruent to 1 mod 24(means if 1 is subtracted fom 49 u get 48 which is divisible by 24)

 so 7^2congruent to 1 mod 24

 so 7^102congruent to 1 mod 24(raising to the power 51)

 hence the remainder when  7^102 is divided by 24 is 1  i.e. 7^102=24m+1

 so multipling by 7 both sides we have....7^103=24.7m+ 7

hence 7^103=24n + 7

so remainder is 7 (ans)


Related Discussions:- Remainder when 7^103 is divided by 24

Word problems, Ana has hiked 4 1/2 miles. She is 2/3 of the way along the t...

Ana has hiked 4 1/2 miles. She is 2/3 of the way along the trail. How long is the trail?

Basics of series - sequences and series, Series - The Basics That top...

Series - The Basics That topic is infinite series.  So just define what is an infinite series?  Well, let's start with a sequence {a n } ∞ n=1 (note the n=1 is for convenie

''t'' distribution, The 't' distribution is a theoretical probability distr...

The 't' distribution is a theoretical probability distribution. The 't' distribution is symmetrical, bell-shaped, and to some extent similar to the standard normal curve. It has an

Evaluating functions, Next we have to talk about evaluating functions.  Eva...

Next we have to talk about evaluating functions.  Evaluating a function is in fact nothing more than asking what its value is for particular values of x. Another way of looking at

Undamped - forced vibrations, We will firstly notice the undamped case. The...

We will firstly notice the undamped case. The differential equation under this case is, mu'' + ku  = F(t) It is just a non-homogeneous differential equation and we identify h

The service was wonderful how much is a 20% tip, Melisa and Jennifer threw ...

Melisa and Jennifer threw a fiftieth birthday party for their father at a local restaurant. While the bill came, Melisa added a 15% tip of $42. Jennifer said in which the service w

Calculate the probability, Given the following decision tree, perform the t...

Given the following decision tree, perform the tasks listed below  1. Simulate the route through the test market and produce results for twenty simulations, calculating the

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd