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(31^31)^728/9.. what is the remainder?
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- (27+4)^31^728
since 27 is divisible completely by 9,we calculate remainder when 4^31^728 is divided by 9
4%9=4
4^2%9=7
4^3%9=1
4^4%9=4
and thus cycle repeats at 4,7,1
31*728=22568
22568%3=2
so ans would be 4^2 % 9=7 - 11 years agoHelpfull: Yes(20) No(2)
- ((31)^31)^728/9
= ((9*3+4)^31)^728)/9=((4)^31)^728/9
=((4)^3*4)^728/9=((64)^10*4)^728/9=((9*7+1)^10*4)^728/9=(4)^728/9
=((4)^3)^242*4^2/9 = 4^2/9
=16/9 = 7(remainder) - 11 years agoHelpfull: Yes(13) No(8)
- 31*31*728 =
4 , 4, -1
-16.
ans is 7
short process
- 11 years agoHelpfull: Yes(7) No(2)
- answer will be 4
(31^31)^728/9
so 31/9= reminder 4
so (4^31)^728/9
so (4*4^30)^728/9= 4*(4^2)^15^728/9=4*(16^15)^728/9
so 16/9= reminder 7
4*(7^15)^728/9= 4*7*(7^14)^728/9=4*7(4^7)^728/9=4*7*4*(4^6)^728/9=4*7*4(7^3)^728/9=4*7*4*7(4^728)/9= reminder 4 - 11 years agoHelpfull: Yes(6) No(13)
- answer-7.
explanation-->(31^31)^728/9 can be written as (4^31)^728/9
now 4 when divided by 9 has got a cycle of 3.now 728x31=22568 which on dividing by 3 gives 2 as remainder which means that the second term in the cycle i.e 4^2 mod 9=7 is the answer.
- 11 years agoHelpfull: Yes(6) No(0)
- By using power cycles concept 31^11 will lead to 31 in last 2 digits thus we can convert the given expression to (31^11*31^11*31^9)^729/9 thus the last 2 digits will be (31*31*31^9)^729/9=31^729/9=(31^11*66)*31^2/9=31^3/9=29791/9 thus the remainder is 1
- 11 years agoHelpfull: Yes(4) No(7)
- (31^31)^728=31^22868/9= 4^22868/9=7
- 11 years agoHelpfull: Yes(3) No(2)
- 31^31=961^728=(960+1)^728=1^728/9=1
- 11 years agoHelpfull: Yes(2) No(12)
- (31^1)^2/9=7 is the remainder
- 11 years agoHelpfull: Yes(2) No(0)
- ans will be 4
((27+4)^31)^728/9
=(4^31)^728
(4^31)%9=4
(4^728)%9=4
so ans 4 - 11 years agoHelpfull: Yes(1) No(8)
- answr is 7
- 11 years agoHelpfull: Yes(1) No(1)
- answer will be 7.
- 11 years agoHelpfull: Yes(0) No(5)
- (31^31)^728 /9 rem=1
31^4/9=29791/9 rem=1
also rem (31^4)^31*182=(1)^(31*182)= rem =1
ans rem=1 - 11 years agoHelpfull: Yes(0) No(1)
- 31=27+4
(27+4)^31^728/9
(4)^31^728/9
31%8=7
(4)^7^728
728%4=0
(4)7^0
4^1/9
ans=4 - 11 years agoHelpfull: Yes(0) No(0)
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