perplexus.info :: Numbers : Higher Powers of Eleven

Higher Powers of Eleven (Posted on 2017-05-24)

Let N(x) be the number 122....221 where the digit 2 occurs x times.

Twice in the past we have determined the highest power of 11 that divides N(2001) is 11^3.

What is the smallest x for N(x) to be a multiple of 11^3? What about multiples of 11^4 and 11^5?

See The Solution Submitted by Brian Smith

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re: Analytic Solution

Comment 4 of 4 |

(In reply to Analytic Solution by Brian Smith)

To continue in this line N(322101) is the minimal term for 11^7.

N=121

Tst=N

Pwr=0

Twos=1

11 Eleven5=11^7

15 do

50 if N%Eleven5=0 then

print Twos;"*"

Ct=Ct+1

endif

80 N=((N-1)*10+21)%Eleven5

Twos=Twos+1

90 loop until Ct>0

----a mess of a program as it was translated into Mintoris Basic.

Posted by Charlie on 2017-05-26 15:45:40

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