Find a positive integer N such that the digits of N combined with the digits of N^2 and the digits of N^3 are exactly the digits of N^6.

Extra credit: Find additional solutions, other than multiples of 10.

(In reply to Computer solution by Larry)

>> s=sym(6812920691)
s =
6812920691
>> s2=s^2
s2 =
46415888341855917481
>> s3=s^3
s3 =
316227766075375861547093499371
>> s6=s^6
s6 =
100000000037022636620406882702394078796495463916006377395641

Already we see more zeros in s^6 than in the concatenation of
 s, s^2 and s^3, but let's verify:

>> a1=[char(string(s)) char(string(s2)) char(string(s3))]
a1 =
    '681292069146415888341855917481316227766075375861547093499371'
>> a2=char(string(s6))
a2 =
    '100000000037022636620406882702394078796495463916006377395641'
>> c1=sort(a1)
c1 =
    '000111111111222233333444444555555666666677777778888888999999'
>> c2=sort(a2)
c2 =
    '000000000000000011122222333333444445566666666677777788899999'
>> 

Indeed they don't match.

Posted by Charlie on 2023-10-11 10:28:43