Can You Count Them?

Algebra Level 4

For how many $3$ -digit prime numbers $\overline{abc}$ do we have $b^2-4ac=9$ ?

0 4 2 1 3

1 solution

Kazem Sepehrinia
Jul 25, 2017

Notice that $b^2-4ac$ is a perfect square and makes $ax^2+bx+c$ factor-able. Then $\overline{abc}=10^2 a+10b+c=(10A+B)(10C+D)$ will never be a prime!

Oh wow. I wrote a program with 0<a<10, -1<b<10, 0<c<10, c mod 2 = 1 to get 4 triplets (a,b,c). I didn't thought such an elementary solution exists. What's more surprising is that I didn't notice that b^2-4ac represents the quadratic discriminant . This is totally unacceptable of me!

Pi Han Goh - 3 years, 10 months ago

Unbelievable! What are you up to? Pull yourself together man :))

Kazem Sepehrinia - 3 years, 10 months ago

Staying up all night. Distracting myself with problems on Brilliant!

Pi Han Goh - 3 years, 10 months ago

@Pi Han Goh – You took it seriously! I'm just kidding :))

Kazem Sepehrinia - 3 years, 10 months ago

Can You Count Them?

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