Cyclic Permutation of Kaprekar Number/Examples

Examples of Cyclic Permutation of Kaprekar Number

972

$972$ is a cyclic permutation of the $3$-digit Kaprekar number $297$.

Thus we have:

\(\ds 972^2\)

\(=\)

\(\ds 944 \, 784\)

\(\ds 944 + 784\)

\(=\)

\(\ds 1728\)

\(\ds 1 + 728\)

\(=\)

\(\ds 729\)

and it is seen that $729$ is another cyclic permutation of $297$.

$\blacksquare$

2727

$2727$ is a cyclic permutation of the $4$-digit Kaprekar number $7272$.

Thus we have:

\(\ds 2727^2\)

\(=\)

\(\ds 7 \, 436 \, 529\)

\(\ds 743 + 6529\)

\(=\)

\(\ds 7272\)

and it is seen that $7272$ is a (trivial) cyclic permutation of $7272$.

$\blacksquare$