Smith numbers

Smith numbers, first defined by Albert Wilanski, are composite num- bers the sum of whose digits are equal to the sum of the digits in an extended prime factorization. For example, 27 is a Smith number since 27 = 3 x3x3 and 2 +7 = 3 + 3 + 3. In addition, 319 = 11 x 29 is a Smith number since 3 + 1 + 9 = 1 + 1 + 2 + 9. The pair 728 and 729 are consecutive Smith numbers. It is an open question whether there are an infinite number of Smith numbers. Wilanski noted, in 1982, that the largest Smith number he knew of belonged to his brother-in-law,H. Smith, whose phone number was 4 937 775. Show that 4 937 775 is a Smith number.

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Comments

The sum of the digits of 4937775 is $4+9+3+7+7+7+5 = 42$ .

Let's factorize! Firstly, the number is divisible by 25 since it ends in 75.
$4937775 \div 25 = 987555 \div 5 = 197511$
This is divisible by 3
$197511 \div 3 = 65837$

$4937775 = 3 \cdot 5^2 \cdot 65837$

$3+5+5+6+5+8+3+7 = 42$

Which proves the fact that 4937775 is a Smith number.

Henry U - 2 years, 4 months ago

It's correct

chakravarthy b - 2 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$