Euclid's formula concerning perfect numbers, progressively developed for all values of n -except 1- produces numbers whose last ciphers are cyclic: 6-6-8-0.
n=2, perfect number = 6 - last cipher 6,
n=3, perfect number = 28- last cipher 8,
n=4, number = 120- last cipher 0,
n=5, perfect number = 496- last cipher 6,
n=6, number = 2016- last cipher 6,
n=7, perfect number = 8128- last cipher 8,
n=8, number = 32640- last cipher 0,
n=9, number = 130816- last cipher 6,
n=10, number = 523776- last cipher 6,
n=11, number = 2096128- last cipher 8,
n=12, number = 8386560- last cipher 0.
Thus, being p = n always an odd number, all perfect numbers have either 6 or 8 as last ciphers. This way the conjecture about 6 or 8 (of Teone da Smirne) as last numbers is clerly demonstrated.
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