Recent content by numbthenoob

Ok, thanks for your insight. Now that I know what relationships to look for, I'm confident that if I dink around with these numbers enough, I'll be able to find them. :-)

Thanks CR, that's a little more on point for what I was straining to get at in my clumsy awkward way...so each divisor has its own set of properties which may or may not yield clues about what factors it can have...interesting.

So you are saying it's because 4 is a small number with a limited number of cases that just happen to work out that way? I.e., no larger number has the same property because it's too large? Is this property for 4 related to it being even? Square? A power of two? Or is there no general theory on...

Hi, Can anyone confirm for me whether it has been proven that: if a number is congruent to 1 mod 4 and is expressed as the product of two factors, the difference between those factors will always be congruent to 0 mod 4; and that if the number is congruent to 3 mod 4 the difference between...

Oh, okay. Awesome, thanks.

Hi Tim, thanks for the reply. Would you mind elaborating a little more on your remarks? I'm not seeing how (2-1)/2 equals 2 for mod 3 and 6 for mod 11. Doesn't it equal one half? Or are you saying that in order to derive a remainder for m for 2x+1 from x, you double the remainder m leaves...

Let T represent an odd target number to be factored. Let m represent any odd number > 1. If T is congruent to zero mod m, (T-1)/2 is congruent to (m-1)/2 mod m, and vice-versa. For example T 35 = 0 mod 5, 17 = 2 mod 5 77 = 0 mod 7, 38 = 3 mod 7 77 = 0 mod 11, 38 = 5 mod 11 47 = 0...

Thanks Office Shredder and Gib Z, those were both very enlightening comments.

Thanks, Dickfore, that was of interest, even if most of it was over my head. However, if I understand correctly...Euler's theorem is about the relationship between coprimes. I'm researching numbers that are not coprime, for example 7! and 72, where the gcd is 7, not 1. To take another...

Is there a name and/or proof for the following conjecture? "For any prime p, p! is congruent to p2-p modulo p2." Thanks much.