More Fun With Num3ers: Calculate your age in days

More Fun With Num3ers: Calculate your age in days: "You can calculate your age in days at ... http://www.derbyshireguide.co.uk/young.htm (1) Is your number a prime number or a composite number..."

Calculate your age in days

You can calculate your age in days at ...

http://www.derbyshireguide.co.uk/young.htm

(1) Is your number a prime number or a composite number?

Here's a list of the First 10,000 Prime Numbers

http://primes.utm.edu/lists/small/10000.txt

A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.

A composite number is a positive integer which has a positive divisor other than one or itself.

Example:

9 can be divided evenly by 1, 3 and 9. So 9 is a composite number.

7 cannot be divided up evenly. we could have divided 7 into seven 1s, or one 7

(2) Is your number a square? cubic? or something else?

More Fun With Num3ers: Waring's problem for cubes

More Fun With Num3ers: Waring's problem for cubes: "Waring's problem for cubes : Every positive integer can be written as the sum of nine (or fewer) positive cubes. 6 = 1^3 + 1^3 + 1^3 + 1^3 ..."

Waring's problem for cubes

Waring's problem for cubes : Every positive integer can be written as the sum of nine (or fewer) positive cubes.

6 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3

7 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3

8 = 2^3

9 = 2^3 + 1^3

10 = 2^3 + 1^3 + 1^3

11 = 2^3 + 1^3 + 1^3 + 1^3

12 = 2^3 + 1^3 + 1^3 + 1^3 + 1^3

13 = 2^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3

14 = 2^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3

15 = 2^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3

23 = 2^3 + 2^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3.

24 = 2^3 + 2^3 + 2^3

29 = 3^3 + 1^3 + 1^3

31 = 3^3 + 1^3 + 1^3 + 1^3 + 1^3

51 = 3^3 + 2^3 + 2^3 + 2^3

Based on this, is it reasonable to suppose that every integer is the sum of nine positive cubes (or fewer) ?

23 is written as the sum of nine positive cubes. Can you find other numbers which can be written as the sum of nine positive cubes?

More Fun With Num3ers: Integers that are both perfect squares and cubes

More Fun With Num3ers: Integers that are both perfect squares and cubes: "64 is the first number after 1 to be both a square and a cube: 64 = 8^2 = 4^3. Let's find few others. The On-Line Encyclopedia of Integer Se..."

Integers that are both perfect squares and cubes

64 is the first number after 1 to be both a square and a cube: 64 = 8^2 = 4^3.

Let's find few others.

The On-Line Encyclopedia of Integer Sequences gives

http://www.research.att.com/~njas/sequences/index.html?q=0,+1,+64,+729,+4096,+15625&language=english&go=Search

0, 1, 64, 729, 4096, 15625, 46656, 117649, 262144, 531441, 1000000, 1771561, 2985984, 4826809, 7529536, 11390625, 16777216, 24137569, 34012224, 47045881, 64000000, 85766121, 113379904, 148035889, 191102976, 244140625, 308915776

0 = 0^3 = 0^2

1 = 1^3 = 1^2

64 = 4^3 = 8^2

729 = 9^3 = 27^2

4096 = 16^3 = 64^2

15625 = 25^3 = 125^2

46656 = 36^3 = 216^2

117649 = 49^3 = 343^2

etc.

A pattern emerges..... Do you see it?

More Fun With Num3ers: More Fun Facts With Num3ers

More Fun With Num3ers: More Fun Facts With Num3ers: "1 + 3 + 1 = 1^2 + 2^21 + 3 + 5 + 3 + 1 = 2^2 + 3^21 + 3 + 5 + 7 + 5 + 3 + 1 = 3^2 + 4^2, etc... 153 is the sum of the first five factorials..."

More Fun Facts With Num3ers

1 + 3 + 1 = 1^2 + 2^2

1 + 3 + 5 + 3 + 1 = 2^2 + 3^2

1 + 3 + 5 + 7 + 5 + 3 + 1 = 3^2 + 4^2,

etc...

153 is the sum of the first five factorials: 1! + 2! + 3! + 4! + 5! = 153

The 26 letters of the alphabet can make 40,329 * 10^22 different combinations

1961 was the most recent year that could be written upside-down and rightside-up and appear the same. The next year with the same properties is 6009

If you change a $5 bill into all the possible ways (cents,nickels,dimes,quarters,halves and dollars) it would require: 2,305,843,009,213,693,951 different changes

Recreation with the 8x table:

1*8=8 (8);

2*8=16 (1+6=7);

3*8=24 (2+4=6);

4*8=32 (3+2=5);

5*8=40 (4+0=4);

6*8=48 (4+8=12, 1+2=3);

7*8=56 (5+6=11, 1+1=2) ...

11264 = 11 * 2^{6+4} .............. [All digits of the number 11264 are used]

2737 = (2 × 7)^3 – 7 ................. [idem]

Royal V. Heath discovered 1118 + 1881 + 8181 + 8818 = 1181 + 1818 + 8118 + 8881

Reverse that and you get:

1888 + 8118 + 8181 + 1811 = 8188 + 1818 + 1881 + 8111

Both equations remain true if you square all their terms.