Italian MO 2002#P1
- Phlembac Adib Hasan
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Find all $3$-digit positive integers that are $34$ times of their digital sum.
- asif e elahi
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Re: Italian MO 2002#P1
What is digital sum?
- Fatin Farhan
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Re: Italian MO 2002#P1
$34*3*n$
such that n is an integer and $0<n<5$
such that n is an integer and $0<n<5$
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- Fatin Farhan
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Re: Italian MO 2002#P1
Digit sum is the sum of digits.asif e elahi wrote:What is digital sum?
Let $D$ be a three digit number where D=100a+10b+c. Then digit sum of D is $a+b+c$
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- Fahim Shahriar
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Re: Italian MO 2002#P1
$34 \times (a+b+c) = 100a+10b+c$
$\Rightarrow 66a-24b-33c = 0$
$\Rightarrow 11 \times (2a-c) = 8b$
$8b$ will be divisible by $11$ if $b=0$.
Now, $11 \times (2a-c)=0$
$\Rightarrow 2a = c$
So the numbers are $102,204,306,408$.
$\Rightarrow 66a-24b-33c = 0$
$\Rightarrow 11 \times (2a-c) = 8b$
$8b$ will be divisible by $11$ if $b=0$.
Now, $11 \times (2a-c)=0$
$\Rightarrow 2a = c$
So the numbers are $102,204,306,408$.
Name: Fahim Shahriar Shakkhor
Notre Dame College
Notre Dame College