Binomial Therom

Ques) The greatest integer whiich divides the number 101 ¹⁰⁰ -1 is:
(a) 100 (b) 1000 (c) 10000 (d) 100000

2 Answers

106

Asish Mahapatra ·2009-10-24 06:00:40

101^1^0^0- 1 =( 100+1)^{100}-1

( 100+1)^{100}-1 = 1 + 100*100 + ^{100}C_{2}.100^2 + ... -1

( 100+1)^{100}-1 = 10^4 (I)\; where \; I \:is \; an\;integer

Thanx a lot Asish

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