The Universe of Discourse Tue, 20 Jun 2006  484848 is excellent
First let's define the items we're talking about:        • It's
obvious, or even if not,   • it follows from an easy inductive
proof, which   • is left as an exercise for the reader.   4bi+1
- 7ai+1= 400bi + 192 - 700ai - 588= 400bi + 700ai + 192 - 588=
100(4bi - 7ai) - 396= 100·4 - 396= And we are done.   bn2 - an2
= cn   bi+12 - ai+12 = 10000bi2 + 9600bi + 2304 - 10000ai2 -
16800ai - 7056 = 10000ci + 2400(4bi - 7ai) - 4752 = 10000ci +
2400·4 - 4752 = 10000ci + 4848 =          10000ci + 2400(4bi -
7ai) - 4752   10000ci + 4848    2400(4bi - 7ai) - 4752 = 4848
or equivalently:  2400(4bi - 7ai) = 9600  which is equivalent
to:  4bi - 7ai = 4.      [Other articles in category /math]
permanent link  Sun, 18 Jun 2006   Principia Mathematica
(through section 56) Principia Mathematica (through section 56)
with kickback no kickback Whitehead and Russell's Principia
Mathematica is famous for taking a thousand pages to prove that
1+1=2. Of course, it pro