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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

1 vote
2 answers
2k views

Finding integers whose sum of digits equals the sum of the digits of a multiple of them

For a given integer $x>0$, I need to find all integers $a \in [0, 10^{15}]$ which have the following property: the digit sum of $a$ equals the digit sum of $x\cdot a$. I found this link http://mathwo …