20070625, 19:22  #1 
Apr 2007
Spessart/Germany
2×3^{4} Posts 
Is this to prove/already known?
Hello,
I got this conjecture last night, but my math is not good enough to prove it... if and only if is divisible by then there is a nonnegative Integer k with (= M(k) + 3) another conjecture: if n>1, n odd then is divisible by are these conjectures already known/proven? And if not, any idea how to prove them? I got them while looking in a selfcreated file with the (start of) factorisations of numbers of the form: , p prime (I made TF in this file up to 30 bit, if wanted I'll post it). Thanks in advance. mfg Matthias 
20070625, 21:12  #2 
Apr 2007
Spessart/Germany
2·3^{4} Posts 
hmhmhmhm,
something I made wrong. If then n is even, then n1 is odd, then n1 is not divisible by 2 as needed for . I made the division with a ShRorder, so the last bit was ignored. A corrected form of the first conjecture is: if and only if is divisible by then there is a nonnegative Integer k with mfg Matthias 
20070626, 10:58  #3 
Feb 2005
2^{2}×3^{2}×7 Posts 

20070627, 04:26  #4  
Apr 2007
Spessart/Germany
2×3^{4} Posts 
Quote:
1) if why does this imply that for some k? (Probably I miss an easy thought...) 2) if n is even I still don't see why n must have the form , if is divisible by (not only by ). greetings, Matthias 

20070627, 05:35  #5  
Feb 2005
2^{2}·3^{2}·7 Posts 
Quote:
If then , and I showed that the latter congruence implies n=2^(k+1)+2 for some k. 

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