[jacks]

Finding all natural number ordered pair \[ (x,y) \] in \[ \displaystyle \binom{x}{y}=2023 \]

[electron]

Hi.

Spoiler

Take a look at Pascal's triangle. If you try \( \binom{x}{1}=\binom{x}{x-1} \) you can see all numbers under and above are different from them. In particular, \( \binom{2023}{1}=\binom{2023}{2022}=2023 \) are the only options we have to verify the equation.

[cerrar]

Regards

[jacks]

Thanks electron got it.