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Two Sums of Two Squares (Posted on 2020-07-17) Difficulty: 2 of 5
Prove that a positive integer n is the sum of two perfect squares if and only if 2*n is also the sum of two perfect squares.

No Solution Yet Submitted by Brian Smith    
Rating: 4.5000 (2 votes)

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Hints/Tips re(2): solution | Comment 3 of 4 |
(In reply to re: solution by Steve Herman)

Two remarks:

1.To avoid ambiguity the word β€œand” should be replaced by a β€œ+” plus sign.  
2.It would be beneficial to address the case of i =0 since it looks funny inserting zero in all equations while obviously 2p=K^2+k^2 implies p=k^2+0 and vice versa .   

Edited on July 20, 2020, 1:33 pm
  Posted by Ady TZIDON on 2020-07-20 13:28:45

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