Digital Root Property

Number Theory Level 3

Given d ( x ) d(x) to be defined to be the digital root of x x in Base 2019 2019 .

If d ( n ) = m d(n) = m , where m = 314 m = 314 (Base 10 10 ), what could the value of n n NOT be in Base 10 10 ?

14440 10404 11044

Timothy Cao by Timothy Cao , 21, Canada

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1 solution

Chris Lewis
Mar 27, 2019

In base 10 10 , a number and its digital root are congruent modulo 9 9 . Likewise, in base 2019 2019 , a number and its digital root are congruent modulo 2018 2018 .

We have 11044 ≡ 954 11044 \equiv 954 , 14440 ≡ 314 14440 \equiv 314 and 10404 ≡ 314 ( m o d 2018 ) 10404 \equiv 314 \pmod{2018} , so the answer is 11044 \boxed{11044} .

3 Helpful 0 Interesting 0 Brilliant 0 Confused

confirmed via wolfram it was easy to see that one of these numbers didnt match the other two

Kyle T - 2 years, 2 months ago

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