the largest number among the following that will perfectly divide (101)^5-1
a) 10 b)1000 c) 500 d) 100
plz explain it properly
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The largest number amongst the following that will perfectly divide 101100–1 is: A. 100 B. 10,000 C. 100100 D. 100,000 Can someone please answer ...
6 votes
HINT Use binomial expansion: (1+100)100−1=(1001)100+(1002)1002+⋯+(100100)100100 So the ... More
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Hint: xn−1=(x−1)(xn−1+xn−2+⋯+1)⏟100 terms Note that 101k≡100k+1(mod1000). ... More
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Using a little "brute force" and calculating mod100000, 1011≡1011012≡102011014≡604011018≡808 ... More
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