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what is the remainder of (16937^30)/31 ?
Read Solution (Total 19)
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- (16937^30)/31
= ((16937%31)^30)%31 i.e (11^30)%31 (by remainder theorem)
= (121^15)%31
=(28^15)%31 =28(784^7)%31
=28(9^7)%31
=28*9*(19^3)%31
=1728468%31=1
- 11 years agoHelpfull: Yes(28) No(1)
- @ JIGNESHKORADIYA
1 is the ans
(16937^30)/31=(15^30)/31(as 15 is the remainder when 16937 is divided by 31)
we can write (15^30)/31 as (225^15)/31
which is equal to (8^15)/31 (as 8 is the remainder when when 225 is divided by 31)
we can write 8^15/31 as (64^7*8/31) = (2^7*8/31) as 2 is remainder when 64 is divided by 31
we can write 2^7*8/31 as ((32*2^2)*8)/31 =(32*32)/31
which when divided by 31 leaves remainder (1*1)/31
so remainder is 1 - 11 years agoHelpfull: Yes(9) No(11)
- 1 is the answer
- 11 years agoHelpfull: Yes(6) No(1)
- answer is 1.consider last two digits 37^30/31= 7^30. odd power even is 1
- 11 years agoHelpfull: Yes(3) No(0)
- by using fermats theorem u can directly get the ans 1.
- 11 years agoHelpfull: Yes(3) No(0)
- ravi kumar,will u pls tell me what is fermest theorem??
- 11 years agoHelpfull: Yes(3) No(0)
- when we divide 16937 by 31 we got 15 as remainder
then we have now (15)^30 so make (15*15) groups of this will result in 15 group
now divide 225/31 we got remainder 8 of 15 times so make (8*8) groups this will result in 7 groups and one 8 extra
now divide 64%31=2
this 2^7 and 2^3= 2^10%31 we got final result 1 - 11 years agoHelpfull: Yes(2) No(5)
- 16937%31=11
11^30=11^28*11^2
11^2=121%31=28
hence ans=28 % =remainder - 11 years agoHelpfull: Yes(2) No(2)
- ans is 1
[sakshi sahni]
(16937^30)/31
= ((16937%31)^30)%31 i.e (11^30)%31 (by remainder theorem)
= (121^15)%31
=(28^15)%31 =28(784^7)%31
=28(9^7)%31
=28*9*(19^3)%31
= 252%31 * 19^2%31
=14*20%31
=so remainder is 1 - 10 years agoHelpfull: Yes(2) No(0)
- i think 30 is the answer to the question
- 11 years agoHelpfull: Yes(1) No(3)
- plz explian any oneeeeeeee
- 11 years agoHelpfull: Yes(1) No(0)
- 1 is the answer
- 11 years agoHelpfull: Yes(1) No(0)
- using remainder theorem ans is 1
- 11 years agoHelpfull: Yes(1) No(0)
- Here on Dividing 16937 by 31 we get 15 ramainder
thus now we can write
((15)^30)/(31)
Now taking 15*15 we can write
((225)^15)/(31)
on Dividing 225 by 31 we get 8 as remainder
so we can write
((8)^15)/(31)
Taking 8*8
((64)^7*8)/(31)
64%31 is 2
so
(2^7*8)/(31)
taking 2^5=32 we can write
(2^5*4*8)/(31)
32%31 is 1
so we are left with
(1*4*8)/(31)
thus it is 32%31=1
so 1 is answer - 10 years agoHelpfull: Yes(1) No(1)
- no not 30 its 24......
- 11 years agoHelpfull: Yes(0) No(3)
- 11 is the ans
- 11 years agoHelpfull: Yes(0) No(1)
- 1 will be the remainder !!!
- 11 years agoHelpfull: Yes(0) No(0)
- use the fermet theorem a^p-1/p =1 where p is a prime number
- 10 years agoHelpfull: Yes(0) No(0)
- Euler thereom says:
a^(p-1)/ p = 1 remainder
where p - prime number
a - natural number
In this question 31 is a prime number
So a^30/31 = 1 remainder - 7 years agoHelpfull: Yes(0) No(0)
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