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the remainder of 2^p/10

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the remainder of 2^p/10

by sanju09 » Sat Apr 30, 2011 1:36 am
If r, s, and t are all positive integers, what is the remainder of 2^p/10 if p = r s t?

(1) s is even.

(2) P = 4 t.
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by clock60 » Sat Apr 30, 2011 2:56 am
got B here my reasoning
(1)if s is even then p is also even as p=r*s*t
then we have two possible remaiders when 2^p/10, 4 or 6 so insuff
(2)p=4t, and p=rst, 4t=rst,sr=4
2^(4*t)/10 will always results in remaider 6 so suff
for futher thinking
2^1=2=10*0+2
2^2=4=10*0+4
2^3=8=10*0+8
2^4=16=10*1+6

2^5=32=10*3+2
we have series of remaiders 2,4,8,6.and every forth exponent will result in reminder 6. our exponent=t*4 ad remaider will always 6
to me suff
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by champmag » Mon May 02, 2011 2:01 am
+1 for B
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