Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 17,470

Approximately 1.444667861.

The number is the highest value of xth root of x for any value of x.

Further,

is finite when x=1 and infinite when x=2.

The maximum value of x such that

is finite is when x=1.444667861 approximately.

The number is eth root of e, where e or the natural logarithm base is approximately 2.7182818284.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 17,470

**Another interesting number:-**

**1787109376.**

**Any power of this number of a number having the last 10 digits as this number will always end in 1787109376, that is, this number.**

**This is true for 6, 76, 376, 9376, 09376, 109376, 7109376, 87109376, 787109376 also.**

**I have given a 10 digit number only. It can be calculated to any number of digits and a number n can be produced containing N digits where any power of n or a number having the last digits as n will always have the last N digits as n.**

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 17,470

A third interesting number is 1152921504606846976.

This is the smallest number apart from zero and one which is a perfect square, cube, fourth, fifth and sixth power.

The number is also a perfect tenth, twelfth, fifteenth, twentieth, thirtieth and sixtieth power.

Character is who you are when no one is looking.

Offline

Pages: **1**