I found an answer from www.quora.com

How to **prove that no positive integer power of 2 ends with four equal** ...

How many **four digit positive integers** have exactly one **digit equal** to **2** and
exactly ... How do you **prove** that **powers** integers of 1.5 are **not equal** to any
**powers** ...

For more information, see How to **prove that no positive integer power of 2 ends with four equal** ...

I found an answer from www.smithsonianmag.com

The Great Debate Over Whether 1+**2**+3+**4**..+ ∞ = -1/12 | Smart News

Jan 31, 2014 **...** Can the sum of all **positive integers** = -1/12? ... of all **positive integers**, that is, 1 +
**2** + 3 + **4** + 5 + 6 +... and so on to infinity is **equal** to. ... Their **proof** seems rock
solid. ... You can add an infinite series of positive **numbers**, and they'**ll** add up to a
**negative** fraction,” said Plait. ... But that's **not the end** of the story.

For more information, see The Great Debate Over Whether 1+**2**+3+**4**..+ ∞ = -1/12 | Smart News

I found an answer from www.khanacademy.com

Intro to the imaginary **numbers** (video) | Khan Academy

He then gets to know this special number better by thinking about its **powers**. ...
How can i^**2** be **equal** to a **negative number** if a square cannot **equal** a **negative**?
..... Counting up by multiples of **4** can be achieved by dividing by **4**. ..... And then
lets **finish** off, well we could keep going on this way We can keep putting high and
...

For more information, see Intro to the imaginary **numbers** (video) | Khan Academy

I found an answer from www.bbc.com

**Positive** and **negative numbers** - Revision **2** - KS3 Maths - BBC ...

Learn about and revise **positive** and **negative numbers** and how to add and
subtract or multiply and divide them with BBC Bitesize KS3 ... Imagine moving up
and down a **number** line to get to the answer. Starting from zero, count up to {**4**} .

For more information, see **Positive** and **negative numbers** - Revision **2** - KS3 Maths - BBC ...

I found an answer from www.britannica.com

perfect **number** | Definition & Facts | Britannica.com

The smallest perfect number is 6, which is the sum of 1, **2**, and 3. ... Perfect
number, a **positive integer** that is **equal** to the sum of its proper divisors. ... For
example, 1 + **2** + **4** = 7 is prime; therefore, 7 × **4** = 28 (“the sum multiplied into the
last”) is a perfect number. ... It is **not** known whether there are any odd perfect
**numbers**.

For more information, see perfect **number** | Definition & Facts | Britannica.com

I found an answer from en.wikipedia.org

Square **number** - Wikipedia

This is also **equal** to the sum of the first n odd **numbers** as can be seen in ... A
**positive integer** can be represented as a sum of two squares precisely if its prime
factorization contains **no** odd **powers** of primes of the form 4k + 3. ... in 1;; if a
number is divisible by **2**, but **not** by 3, its square **ends** in **4**; and; if a ...

For more information, see Square **number** - Wikipedia

I found an answer from math.stackexchange.com

**Prove** that a square of a **positive integer** cannot end with **4** same ...

Assume that a **number** x ∈ N suffices x **2** mod 10000 = 4444 . Notice that only the
**4** least significat **digits** of x are important for computing x **2** mod 10000 , so ...

For more information, see **Prove** that a square of a **positive integer** cannot end with **4** same ...

I found an answer from mathworld.wolfram.com

Square **Number** -- from Wolfram MathWorld

Lagrange's **four**-square theorem), that every "sufficiently large" **integer** is a sum of
**no** more than **4 positive** squares ( G(**2**)=**4** ) ... In general, **proving** that only certain
**numbers** are simultaneously figurate in two ... The answer is that the **number**
**ends** in the **digit** "**2**," which is **not** one of the possible last **digits** for a square
**number**.

For more information, see Square **Number** -- from Wolfram MathWorld