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

What is the surface area of a ball with a diameter of 6 inch, The formula f...

The formula for the surface area of a sphere is 4πr 2 . What is the surface area of a ball with a diameter of 6 inches? Round to the nearest inch. (π = 3.14) If the diameter  o

#title.automotive cruise control system., What are some of the interestingm...

What are some of the interestingmodern developments in cruise control systems that contrast with comparatively basic old systems

Factors, Question Suppose that f(x) has (x - 2) 2 and (x + 1) as its on...

Question Suppose that f(x) has (x - 2) 2 and (x + 1) as its only factors. Sketch the graph of f. State all the zeros of f.

Proof by Condratiction, "Prove by contradiction that no root of the equatio...

"Prove by contradiction that no root of the equation x^18 -2x^13 + x^5 -3x^3 + x - 2 = 0 is an integer divisible by 3" Any help would be very much appreciated!

Prove that prims algorithm produces a minimum spanning tree, Prove that Pri...

Prove that Prim's algorithm produces a minimum spanning tree of a connected weighted graph. Ans: Suppose G be a connected, weighted graph. At each iteration of Prim's algorithm

Which kevin gets paid is represented by x what does paid, Patrick gets paid...

Patrick gets paid three dollars less than four times what Kevin gets paid. If the number of dollars which Kevin gets paid is represented through x, what does Patrick get paid?

Some important issue of graph, Some important issue of graph Before mov...

Some important issue of graph Before moving on to the next example, there are some important things to note. Firstly, in almost all problems a graph is pretty much needed.

50+50, what is the totel

what is the totel

Common graphs, Common Graphs : In this section we introduce common graph o...

Common Graphs : In this section we introduce common graph of many of the basic functions. They all are given below as a form of example Example   Graph y = - 2/5 x + 3 .

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