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clarified the question according to the comments
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Guntram
Guntram
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Sum Finding integers whose sum of digits of number A which equals the sum of the digits of x*Aa multiple of them

For a given integer $x>0$, I need to find all decimal numbers $a1,a2,a3,...,an$ in a range [0;integers $10^15$]$a \in [0, 10^{15}]$ which have the following property: the digit sum of $a1$$a$ equals the digit sum of $x*a1$ for any decimal number $x>0$$x\cdot a$.

I found this link http://mathworld.wolfram.com/CastingOutNines.html which looks quite relevant to my task, but I can't figure out how to apply it.

Any ideas?

Sum of digits of number A which equals sum of digits of x*A

I need to find all decimal numbers $a1,a2,a3,...,an$ in a range [0; $10^15$] which have following property: digit sum of $a1$ equals digit sum of $x*a1$ for any decimal number $x>0$.

I found this link http://mathworld.wolfram.com/CastingOutNines.html which looks quite relevant to my task, but I can't figure out how to apply it.

Any ideas?

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://mathworld.wolfram.com/CastingOutNines.html which looks quite relevant to my task, but I can't figure out how to apply it.

Any ideas?

removed irrelevant comm alg tag
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Yemon Choi
Yemon Choi
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added 1 characters in body; edited tags
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Jull
Jull
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I need to find all decimal numbers $a1,a2,a3,...,an$ in a range [0; $10^9$$10^15$] which have following property: digit sum of $a1$ equals digit sum of $x*a1$ where $x$ is somefor any decimal number $x>0$.

I found this link http://mathworld.wolfram.com/CastingOutNines.html which looks quite relevant to my task, but I can't figure out how to apply it.

Any ideas?

I need to find decimal numbers $a1,a2,a3,...,an$ in a range [0; $10^9$] which have following property: digit sum of $a1$ equals digit sum of $x*a1$ where $x$ is some decimal number.

I found this link http://mathworld.wolfram.com/CastingOutNines.html which looks quite relevant to my task, but I can't figure out how to apply it.

Any ideas?

I need to find all decimal numbers $a1,a2,a3,...,an$ in a range [0; $10^15$] which have following property: digit sum of $a1$ equals digit sum of $x*a1$ for any decimal number $x>0$.

I found this link http://mathworld.wolfram.com/CastingOutNines.html which looks quite relevant to my task, but I can't figure out how to apply it.

Any ideas?

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Jull
Jull
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