MathDB

We say that a set

S

of natural numbers is synchronous provided that the digits of

a^2

are the same (in occurence and numbers, if differently ordered) for all numbers

a

S

. For example,

\{13, 14, 31\}

is synchronous, since we find

\{13^2, 14^2, 31^2\} = \{169, 196, 961\}

. But

\{119, 121\}

is not synchronous, for even though

119^2 = 14161

and

121^2 = 14641

have the same digits, they occur in different numbers. Show that there exists a synchronous set containing

2021

different natural numbers.

3b