Play with number
Number Theory
Level
3
Find the smallest 6-digit positive integer such that when it is multiplied by 2, 3, 4, 5 or 6, the resultant number is a cyclic permutation of the original number.
The answer is 142857.
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1 solution
N = a b c d e f
If N is multiplied by 6 and it is also a six digit number then a must be 1.
We know 7 1 = 0 . 1 4 2 8 5 7
And it has a property if we miltiply this fraction wth 2,3,4,5,6 it will permute cyclically.
So the number is 142857