Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20130129 11:47:37
squaresA number is called a perfect square if it is the square of an integer. How many pairs of perfect squares differ by 495? (Order does not matter. So, the pair "16 and 9" is the same as "9 and 16".) I see you have graph paper. You must be plotting something #2 20130129 12:19:25
Re: squaresHi; are all solutions of x^2  y^2 = 495 In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #3 20130129 15:12:56
Re: squaresExactly how many are there, I did 24, but it is wrong.. I see you have graph paper. You must be plotting something #4 20130129 17:09:35
Re: squaresYou did not say positive numbers or not. There are 24 positive and negative. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #5 20130130 08:03:22
Re: squaresConsidering just positive integers, there are 6 factorizations of 495 into two factors: If I recall correctly this was involved in one of Fermat's methods of factoring odd composites. Have a grrreeeeaaaaaaat day! Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. 