Set of 7 Anagrams which are Square

Theorem

The following integers are all anagrams, and all square:

$1 \, 048 \, 576, 1 \, 056 \, 784, 1 \, 085 \, 764, 5 \, 740 \, 816, 5 \, 764 \, 801, 6 \, 754 \, 801, 7 \, 845 \, 601$

Proof

\(\ds 1 \, 048 \, 576\)

\(=\)

\(\ds 1024^2\)

\(\ds 1 \, 056 \, 784\)

\(=\)

\(\ds 1028^2\)

\(\ds 1 \, 085 \, 764\)

\(=\)

\(\ds 1042^2\)

\(\ds 5 \, 740 \, 816\)

\(=\)

\(\ds 2396^2\)

\(\ds 5 \, 764 \, 801\)

\(=\)

\(\ds 2401^2\)

\(\ds 6 \, 754 \, 801\)

\(=\)

\(\ds 2599^2\)

\(\ds 7 \, 845 \, 601\)

\(=\)

\(\ds 2801^2\)

$\blacksquare$

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1,048,576$