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Number Theory Level 3

Find the smallest prime that is equal to the product of its digits plus the sum of its digits.


The answer is 19.

Sanyam Goel by sanyam goel , 26, India

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2 solutions

Ashwin K
Feb 11, 2016

Let the 2 digits of the number be ab. 

We can rewrite the question as, ab+a+b = 10a + b.

Solving the equation, we get, b = 9 which means our answer should end in 9.

I see all numbers ending in 9 follow this property. 
Somebody please do some research on this. I need a clarity of how this works.

As per the question, the smallest prime happens to be 19.

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Sanyam Goel
Feb 10, 2016

19 = (1 * 9) + (1 + 9) ..:)

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