Maths is weird, and fun [ongoing]

Maths has surprised me many times. I am listing some of the weird things I remember:

Useful Maths

Division by 2: If the last number is even, the number divides with 2
Division by 3: If the sum of all digits is divisible by 3, the number is divisible by 3
- Ex: 23598 => 2+3+5+9+8 = 27. Since 3 divides 27. 23598 is divisible by 3
Division by 4: If last two digits divide by 4, the number is divisible by 4.
- Ex: In 34342344, last two digits 44 divide by 4. So it's divisible by 4
Division by 5: Last digit is either 5 or 0
Division by 6: Check Division with 2 and 3 independently. If both divisible, then 6 is divisible
Division by 7: This one is easy but difficult to put in a single sentence so search "How to Tell If a Number is Divisible by 7"
Division by 8: Check last 3 digits, for divisibility by 8. If it divides, the number is divisible by 8
Division by 9: Same as 3, add all numbers and check if it's divisible by 9
- Ex: 23598 => 2+3+5+9+8 = 27. Since 9 divides 27. 23598 is divisible by 9
Division by 11: add alternating sum of digits. Check if divisible by 11. If yes, the number is divisible by 11.
- Ex: 123456789, => 1-2+3-4+5-6+7-8+9 = 5. So this number is not divisible by 11.
Interested in checking divisibility with higher numbers? Check savory maths.

The Sum of two odd squares cannot be a square.
If the product of four consecutive integers is increased by 1 the result is a square number. Ex: 1 x 2 x 3 x 4 + 1 = 25 which is 5 square

I have never seen a formula which looks so simple and yet doesn't make any sense at all. Credit goes to Ramanujan.
- The formula is: 1 + 2 + 3 + ..... = - 1/12 . Details here

Do you have anything else to add? Let me know in comments