what is remainder of 16 17 17 16

16^16 * 16^1 / 17^16
(16/17)^16 * 16

We can write 16 as 17*1-1
(17*1-1/17)^16 * 16
(ax-1/a)^n ll always gives remainder 1 ... (ie) a=17, x=1, n=16...
So Remainder = 1
Therefore 1*16 = 16
So Remainder = 16

[Otherwise we can say, a^n/(a+1)^n-1 always gives the remainder a...
For example, a=2, n=3=> 2^3/3^2 = 8/9 => remainder = 8... bcozzz denominator is greater than the numerator... Hence the remainder ll be numerator only...]

Ans : 16
10 years agoHelpfull: Yes(17) No(9)
make common
16*(16/17)^16
16*(-1)^16
16 remainder
10 years agoHelpfull: Yes(8) No(0)
maximum cyclic order of any no is 4
so for 16^17=17/4=reminder 1
so 16
and for 17^16=16/4=reminder 0
so only 16 is remaining
so answer is 16.
10 years agoHelpfull: Yes(7) No(2)
16 is wrong...
Anyone plzzz post the solution for this...
10 years agoHelpfull: Yes(5) No(3)
6.065365311 by making use of calci
10 years agoHelpfull: Yes(3) No(11)
16^17/17^16=(16/17)^16*16
{(17-1)/17}^16*16---R---->
(-1)^16/17^16*16=16/17^16
hence remainder is 16
10 years agoHelpfull: Yes(2) No(1)
(16^17)/(17^16)= (16^16)*16/(17^16)
ie. ((16^16)/17)*(16/(17^15))
now (a^n)/(a+1) is '1' if n is even
and (a^n)/(a+1) is 'a' if n is odd
here n=16=even. so remainder of ((16^16)/17) is 1.
remainder of (16/(17^15)) is always 16.
so the remainder will be 1*16 ie. 16
10 years agoHelpfull: Yes(2) No(3)
((16^16)*16)%(17^16)=((-1)^16)*16)%(17^16)=16%(17^16)=16
10 years agoHelpfull: Yes(1) No(0)
(-1*49)+99=50
10 years agoHelpfull: Yes(0) No(5)

what is remainder of(16^17)/(17^16).