Math Is Fun Forum

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,566

Re: Some special numbers

87) Sum of first Ten Prime Numbers

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,566

Re: Some special numbers

88) 6,469,693,230

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,566

Re: Some special numbers

89) Automorphic Number

In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base b.

Definition and properties

Given a number base b, a natural number n with k digits is an automorphic number if n is a fixed point of the polynomial function

over

,
the ring of integers modulo

As the inverse limit of

is

,
the ring of b-adic integers, automorphic numbers are used to find the numerical representations of the fixed points of

over

.

For example, with b=10, there are four 10-adic fixed points of

, the last 10 digits of which are:

Thus, the automorphic numbers in base 10 are 0, 1, 5, 6, 25, 76, 376, 625, 9376, 90625, 109376, 890625, 2890625, 7109376, 12890625, 87109376, 212890625, 787109376, 1787109376, 8212890625, 18212890625, 81787109376, 918212890625, 9918212890625, 40081787109376, 59918212890625, .... whose square "ends" in the same digits as the number itself.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.