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

Ratio, ther are 162 student in a school.20 of them are girls .how many are ...

ther are 162 student in a school.20 of them are girls .how many are boy

Cenamatic, a tire placed on a balancing machine in a service station starts...

a tire placed on a balancing machine in a service station starts from rest an d turns through 4.7 revolutions in 1.2 seconds before reaching its final angular speed Calculate its a

Algebra, prove That J[i] is an euclidean ring

prove That J[i] is an euclidean ring

Statistical inference, Statistical inference This is the process of dra...

Statistical inference This is the process of drawing conclusions about attributes of a population based upon information contained in a sample or taken from the population.

What is a negative number, Q. What is a Negative Number? Ans. Neg...

Q. What is a Negative Number? Ans. Negative numbers are very important in mathematics. We say that positive and negative numbers are opposites of one another. Here

Continuous random variable, Continuous Random Variable In the probabili...

Continuous Random Variable In the probability distribution the sum of all the probabilities was 1. Consider the variable X denoting "Volume poured into a 100cc cup from coff

Algebra, find the value of A and B if the following polynomials are perfect...

find the value of A and B if the following polynomials are perfect square:

Opt math, howwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww...

howwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww

Market, what is market

what is market

Basic requirement for interpolation & extrapolation to work, What is the ba...

What is the basic requirement for both interpolation and extrapolation to work? There must exist a functional relationship between an independent variable and a dependent variable

Write Your Message!

Name

Email id

Message

Verfication Code

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!

Submit Assignment

User Account

All Pages