11.40 pm

**Fundamental Theorem of Arithmetic**

Any positive integer (except 1) can be written as the product of prime numbers in one and only one way.

**Erdos numbers [Paul Erdos, Hungarian math]**

"Between any whole numbers n and 2n, there must always lie at least one prime" (at his 17 years old... omg!)

**Amicable numbers [Leonhard Euler, 18th century]**

"two whole numbers to be amicable if each was the sum of the proper divisors of the other"

example:

220 = 1,2,4,5,10,11,20,22,44,55,110,220

*(the divisors of 220)*

284 = 1,2,4,71,142,284

*(the divisors of 284)*

then

220 = 1+2+4+71+142

284 = 1+2+4+5+10+11+20+22+44+55+110

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