divisibility by 13?
Number Theory
Level
3
N is a 50 digit number.all the digits except the 26th from the right are 1.If N is divisible by 13, find the unknown digit.
The answer is 9.
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Note that 13 divides 1 1 1 1 1 1 1 1 1 1 1 1 ....SO the number we are considering can be expressed in the form 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 x 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 .Note that 13 divides the expressions i=on both side of x1.....So 13 must divide x 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . . . . 0 . . . So the only possibility is x = 9 ...