An automorphic number survives squaring with its own digits intact at the end: 76² = 5776, 625² = 390625, 9376² = 87909376.
In base 10 there are exactly two nontrivial infinite chains of automorphic numbers, ending in …5 and …6, each extending one digit at a time (5, 25, 625, 0625→90625, …; 6, 76, 376, 9376, …). In the language of p-adic numbers, these chains converge to the two nontrivial solutions of \(x^2 = x\) in \(\mathbb{Z}_{10}\) — a rare place where exotic 10-adic arithmetic shows up in recreational mathematics.