20060221, 16:59  #23  
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·19 Posts 
why not?
Quote:
Its easier when you actually do it. Take for instance the number 125. Half of this is 62.5 Discard the decimal and take the lower integral value as 62.Similarly the higher value is 63 so 63^2  62^2 = 125 Theorem:1: The square of a number is either divisible by 4 or leaves the remainder 1 when divided by 4 Theorem 2: The square of an odd number is of the form 8q + 1 There are interesting proofs of these theorems. Try them out. Mally 

20060222, 14:08  #24  
Aug 2002
Buenos Aires, Argentina
2472_{8} Posts 
Quote:
Starting with an odd integer 2n+1, its square is: (2n+1)^{2} = 4n^{2}+4n+1. Since n^{2} has the same parity of n, this means that n^{2} + n is even, so 4n^{2} + 4n is multiple of 8. Thus the square has the form 8q+1, as expected. 

20060223, 09:54  #25  
"Richard B. Woods"
Aug 2002
Wisconsin USA
1111000001100_{2} Posts 
Quote:
"Conjectured list of positive numbers which are not of the form r^is^j, where r,s,i,j are integers with r>0, s>0, i>1, j>1" Quote:
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So "M is a number that should be in N" is contradictory to "Joe Nobody finds that f(x) = M", and your conclusions after that are invalid. Quote:
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Perhaps you'd care to restate what you mean? 

20060223, 17:27  #26  
Nov 2003
7460_{10} Posts 
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20060223, 17:31  #27  
Nov 2003
1D24_{16} Posts 
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20060223, 17:39  #28  
∂^{2}ω=0
Sep 2002
República de California
3·7·19·29 Posts 
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20060224, 23:32  #29  
Oct 2005
Fribourg, Switzerlan
252_{10} Posts 
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20060225, 03:07  #30  
Dec 2003
Hopefully Near M48
2×3×293 Posts 
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20060306, 23:20  #31 
∂^{2}ω=0
Sep 2002
República de California
3·7·19·29 Posts 
By popular request, I've split the thread  the theological debate which began at this point has been moved to the Soapbox.
Please keep the posts in this thread ontopic (i.e. mathematically oriented). 
20060306, 23:47  #32 
Jun 2003
2^{3}×197 Posts 
Actually some of the later posts were math related also.

20060316, 19:28  #33  
Feb 2003
118_{10} Posts 
Quote:
N in (6,14, ... 426) b < 32, b prime, y < 4*10^7, any x, any a and b < 4000, b prime, y< 400, any x, any a 
