The product of two consecutive positive integers is $156$. The integers are

The product of two consecutive positive integers is $156$. The integers are
  1. $12$ and $13$
  2. $13$ and $14$
  3. $11$ and $12$
  4. $10$ and $13$

Solution

Let integers be $x$ and $x+1$: $x^{2}+x-156=0 \Rightarrow (x+13)(x-12)=0$. Take $x=12$. So $12$ and $13$.

Asked in: IMO

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