Advent calendar 2025

The sum of \(n\) consecutive numbers starting at \(m\) is \(m + (m + 1) + ... + (m + n-1) = nm + 0 + 1 + ... + n - 1\). The sum of the next \(n\) consecutive number is \((m+n) + (m+n+1) + ... + (m + 2n - 1 ) = n(m + n) + 0 + 1 + ... + n - 1\). The difference between these two is \(n(m + n) - nm = n^2\).

Therefore, whatever value of \(m\) is used, \(n\) will always be 451.