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If 10^m divides the number 101^(100)-1 t...

If `10^m` divides the number `101^(100)-1` then, find the greatest value of `mdot`

Text Solution

Verified by Experts

The correct Answer is:
m = 4
`(1+100)^(100) = 1+100 xx 100 + (100 xx 99)/(1 xx 2) xx (100^(2)) + (100 xx 99 xx 98)/(1xx2xx3)xx(100^(3))+"…."`
`rArr (101)^(100) - 1`
`= 100 xx 100 [ 1+(100 xx 99)/(1xx2)+(100xx9xx98)/(1xx2xx3)xx100+"….."]`
From above, it is clear that `(101)^(100) - 1` is divisible by
`(100)^(2) = 10000`. So, the greatest value of m is 4.
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