For some and let be a sequence where:
is a positive integer
Digit sums of all are equal (base )
Can we construct such sequence for any positive integer ( is of your choice)?
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Hint : Prove that their digit sum must be divisible by 9. Knowing that you can show that we can lengthen a given sequence by adding a zero on the end of the first term and then dividing it by 2 (e.g. 9 , 1 8 , 3 6 , 7 2 , 1 4 4 − − > 4 5 , 9 0 , 1 8 0 , 3 6 0 , 7 2 0 , 1 4 4 0 )