I am getting married and quite a few of my guests are mathematicians. I would like to design an invite with a puzzle. Basically, I would like to pose a short puzzle with the answer 26.
My example (but might be too easy (it can be solved with the knowledge of quadratic equation)).
If
$$ a+b = 4 $$ and $$ a^2 + b^2 = 10 $$ then $$ a^3 + b^3 -2 = ? $$
However, it need not be a number theory question. Thank you for your time.
From Wikipedia:
1) Tell me the only integer that is one greater than a square $(5^2 + 1)$ and one less than a cube $(3^3 − 1)$.
2) Find the smallest number $(26)$ that is not a palindrome whose square is a palindrome $(26^2 = 676)$.