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 symmetric value, What is symmetric value

What is symmetric value

Which mathematical property did marty use to get similar ans, Marty used th...

Marty used the subsequent mathematical statement to show he could change an expression and still get the similar answer on both sides: 10 × (6 × 5) = (10 × 6) × 5 Which mathematica

Complex number, The points A,B,C and D represent the numbers Z1,Z2,Z3 and Z...

The points A,B,C and D represent the numbers Z1,Z2,Z3 and Z4.ABCD is rhombus;AC=2BD.if Z2=2+i ,Z4=1-2i,find Z1 and Z3 Ans) B(2,1) , D(1,-2) Mid Point (3/2,-1/2) Write Equati

Find the sum of all 3 digit numbers which leave remainder 3, Find the sum o...

Find the sum of all 3 digit numbers which leave remainder 3 when divided by 5. Ans: 103, 108..........998 a + (n-1)d = 998

Coefficient of correlation denoted, Coefficient of Correlation Denoted ...

Coefficient of Correlation Denoted There are two methods which measure the degree of correlation among two variables these are denoted by R and r. (a) Coefficient of correl

What is the difference between the two models listed above?, E1) What is th...

E1) What is the difference between the two models listed above? Which is more difficult for children to understand? E2) List some activities and word problems that you would exp

F distribution or variance ratio distribution, Frequency Distribution or Va...

Frequency Distribution or Variance Ratio Distribution This was developed by R. A Fisher in 1924 and is normally defined in terms of the ratio of the variances of two usually d

Integers, hi i would like to ask you what is the answer for [-9]=[=5] grade...

hi i would like to ask you what is the answer for [-9]=[=5] grade 7

If the area of the parallelogram is 36 m2 what is the height, The height of...

The height of a parallelogram measures 5 meters more than its base. If the area of the parallelogram is 36 m 2 , what is the height in meters? Let x = the measure of the base a

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

Write Your Message!

Name

Email id

Message

Verfication Code

User Account

All Pages