- Is there a conjecture that states that every even number can be expressed

as the sum of powers of 2 ?

42 = 32 + 8 + 2

Powers of 2 that weren't used to get to 42..

4,16

The next power of 2 over 42 is 64. If we go 64 - 16 -4 we should

get 44 ( we always end up with the number +2)

134 = 2+4+128

powers that weren't used...

136 = 256 - (16+32+64+8)

Markus - Never mind, I suppose we can call this the binary number system!

At 12:12 AM 6/1/2002 -0700, Markus Frind wrote:>Is there a conjecture that states that every even number can be expressed

>as the sum of powers of 2 ?

>

>42 = 32 + 8 + 2

>

>Powers of 2 that weren't used to get to 42..

>4,16

>

>The next power of 2 over 42 is 64. If we go 64 - 16 -4 we should

>get 44 ( we always end up with the number +2)

>

>134 = 2+4+128

>

>powers that weren't used...

>136 = 256 - (16+32+64+8)

>

>

>Markus

>

>

>

>Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com

>The Prime Pages : http://www.primepages.org

>

>

>

>Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/ - In message <5.0.0.25.2.20020531235709.033ebba0@...>, Markus

Frind <flames@...> writes>Is there a conjecture that states that every even number can be expressed

Well, yes. If you used bit 0 as well, you would find that two's

>as the sum of powers of 2 ?

>

>42 = 32 + 8 + 2

>

>Powers of 2 that weren't used to get to 42..

>4,16

>

>The next power of 2 over 42 is 64. If we go 64 - 16 -4 we should

>get 44 ( we always end up with the number +2)

>

>134 = 2+4+128

>

>powers that weren't used...

>136 = 256 - (16+32+64+8)

complement arithmetic worked properly without being out by two.

--

Ben