Square Number ending in 9 Digits in Reverse Order

Theorem

The next integer after $1 \, 111 \, 111 \, 111$ whose square ends in $987 \, 654 \, 321$ is:

$2 \, 380 \, 642 \, 361^2 = 5 \, 667 \, 458 \, 050 \, 987 \, 654 \, 321$

Proof

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Historical Note

According to David Wells, in his Curious and Interesting Numbers of $1986$, this factoid was noted by J.A.H. Hunter, but this needs to be corroborated.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1,111,111,111,111,111,111$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1,111,111,111,111,111,111$