Sum of Two Squares

09102021, 04:05 PM
(This post was last modified: 09102021 05:52 PM by Albert Chan.)
Post: #7




RE: Sum of Two Squares
(09102021 02:55 PM)Albert Chan Wrote: Another example, from "Dead Reckoning", p65, (k = 22) Another way, by forcing k=1 ... radical will disappear. 1457 = 37^2 + (2√22)^2 = 7^2 + (8√22)^2 gcd(1457, 30^2+(6√22)^2 = 1692 = 1457+5*47) = 47 This work even for sum of square of radicals. 1457 = 3*2^2 + 5*17^2 = (2√3)^2 + (17√5)^2 1457 = 3*22^2 + 5*1^2 = (22√3)^2 + (√5)^2 gcd(1457, (20√3)^2+(16√5)^2 = 2480 = 2^4*5*31) = 31 Interestingly, gcd(n, a*d ± b*c) seems to work as well. gcd(1457, 2*117*22 = 372 = 2^2*3*31) = 31 gcd(1457, 2*1+17*22 = 376 = 2^3*47) = 47 

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Messages In This Thread 
Sum of Two Squares  Eddie W. Shore  08172019, 01:35 PM
RE: Sum of Two Squares  klesl  08172019, 07:05 PM
RE: Sum of Two Squares  Eddie W. Shore  08202019, 05:25 AM
RE: Sum of Two Squares  Eddie W. Shore  08182019, 05:27 PM
RE: Sum of Two Squares  Albert Chan  09092021, 11:12 PM
RE: Sum of Two Squares  Albert Chan  09102021, 02:55 PM
RE: Sum of Two Squares  Albert Chan  09102021 04:05 PM

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