MathDB

Let

b\ge 2

be an integer. Call a positive integer

n

b

-eautiful if it has exactly two digits when expressed in base

b

and these two digits sum to

\sqrt{n}

. For example,

81

13

-eautiful because

81 = \underline{6} \ \underline{3}_{13}

and

6 + 3 = \sqrt{81}

. Find the least integer

b\ge 2

for which there are more than ten

b

-eautiful integers.

Problem Statement