Other possible details include startup funds (e.g. US$1M over 10 years), lab space (dry/wet lab, exclusive use square footage), and access to shared facilities (big experimental equipment). Lab space and shared facilities aren't free, so the cost is often deducted from your startup funds.
The first few abundant numbers are 12, 18, 20, 24, 30, 36, 40, 42, 48, ... Note that most of these appear to be even; the first odd one does not appear until 945. This is quite remarkable, as it provides a naturally occurring example of a large number. After 945, the odd-abundant numbers are 1,575, 2,205, 2,835, 3,465, ...
(b) Use either a proof by contraposition or a proof by contradiction to show that if m and n are integers and mn is even, then m is even or n is even. Answer: An odd number is one of the form 2n+1, where n is an integer.We are given two odd numbers, say 2a+1 and 2b+1. Their product is: (2a+1)(2b+1) = 4ab + 2a + 2b + 1 = 2(2ab + a + b) + 1This last expression shows that the product is odd, since it is of the form 2n+1, with n = 2ab + a + b.b) Use either a proof by contraposition or a proof by contradiction to show that if m and n are integers and mn is even, then m is even or n is even. Answer: An odd number is one of the form 2n+1, where n is an integer.