So this page is merely the first stage. A lot more laws will need to be added here so if you know of a law or mathematical fact that you think should be listed here than please email me.
| Any multiple of a perfect number or an abundant number is also abundant. Every number greater than 20161 can be expressed as a sum of two abundant numbers. |
| The nth cubic number is a sum of n consecutive odd numbers, for example 1cubed=1, 2cubed=3+5, 3cubed=7+9+11 and 4cubed=13+15+17+19. |
| The sum of the first n odd numbers is a Square Number, for example 1=1, 4=1+3, 9=1+3+5 and 16=1+3+5+7. |
| Any positive integer can be represented in exactly one way as a product of primes. |
| Every positive integer is a sum of at most three triangular numbers. |
| Every positive integer can be written as the sum of at most four squares. |
| The total number of 1s that occur among all unordered partitions of a positive integer is equal to the sum of the numbers of distinct members of those partitions. |
| Reichert and Toepkin (1940) proved that a rectangle cannot be dissected into fewer than nine different squares.
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| It is impossible to fill a rectangular box with a finite number of unequal cubes.
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| No odd Fibonacci number is divisible by 17
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| All integers are the sum of at most 27 prime numbers.
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| Every positive whole number can be written as the sum of eight cubes (including 0^3 when necessary) EXCEPT 23 and 239. Those two numbers require 9 cubes.
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| Every number is the sum of at most 7 octahedral numbers. |
| There are exactly nine Heegner numbers: 1, 2, 3, 7, 11, 19, 43, 67, 163. |
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Except for 2 and 3, every prime number will eventually become divisible by 6 if you either add or subtract 1 from the number. For example, the number 17, plus 1, is divisible by 6. The number 19, minus 1, is also divisible by 6.
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