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

Reduction formulae, assigenment of b.sc. 1st sem

assigenment of b.sc. 1st sem

Applications of series - estimating the value of a series, Estimating the V...

Estimating the Value of a Series One more application of series is not actually an application of infinite series. It's much more an application of partial sums. Actually, we

Positive exponents, Simplify following and write the answers with only posi...

Simplify following and write the answers with only positive exponents. (-10 z 2 y -4 ) 2 ( z 3 y ) -5 Solution (-10 z 2 y -4 ) 2 ( z 3 y ) -5

Describe the laws of sines, Q. Describe the Laws of Sines? Ans. Up...

Q. Describe the Laws of Sines? Ans. Up to now we have dealt exclusively with right triangles. The Law of Sines and the Law of Cosines are used to solve oblique triangles

Quan. literacyprofiency, 3.20 euros per kilogram, 1 kilogram =2.2 pounds an...

3.20 euros per kilogram, 1 kilogram =2.2 pounds and current exchange rate is $1=0.9 euros. what is the price per pound?

Area related to circles, railway tunnel of radius 3.5 m and angle aob =90 f...

railway tunnel of radius 3.5 m and angle aob =90 find height of the tunnel

How to add mixed numbers, Q. How to Add Mixed Numbers? Ans. If you...

Q. How to Add Mixed Numbers? Ans. If you have to add mixed numbers, you might try this method first: First rewrite the mixed number as a whole number plus a fracti

Quantitative Techniques, The following table given the these scores and sal...

The following table given the these scores and sales be nine salesman during last one year in a certain firm: text scores sales (in 000''rupees) 14 31 19

Calculus, I need help with my calculus work

I need help with my calculus work

Local maxima, Given that f(x,y) = 3xy - x 2 y - xy 2 . Find all the poin...

Given that f(x,y) = 3xy - x 2 y - xy 2 . Find all the points on the surface z = f(x, y)where local maxima, local minima, or saddles occur

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