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

You are not logged in. #1 20081128 05:56:55
Number theory proofProve that if then 60xyz (where x, y and z are positive integers).#2 20081128 13:40:28
Re: Number theory proofPythagorean triples are of the form where are positive integers with . So we want to show that is divisible by 30, i.e. by 2, 3 and 5. 2 N is even if one of a and b is even. If they’re both odd, then their sum is even, so N is again even. 3 If neither a nor b is divisible by 3, then one of the following happens: In cases (i) and (ii), ; in case (iii), . 5 Suppose , . Then by Fermat’s little theorem, ; . QED. Last edited by JaneFairfax (20081128 13:56:23) #3 20081129 01:22:53
Re: Number theory proofNice I did it slightly differently. I considered the possible values of x, y and z mod 3, mod 4 and mod 5. 