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How many positive integers $n$ less than $100$ can be expressed in the form $ab + a + b,$ where $a,b$ are positive integers?

I wasn't quite sure how to approach this problem besides simply finding values for all the numbers or making a table, so is there a slicker solution? Thanks.

questionasker
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1 Answers1

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Hint: $ab+a+b=(a+1)(b+1)-1$ so the numbers $n$ that can be expressed in that form are exactly those for which $n+1$ is not prime.

leoli1
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