Sum of two squares

Number Theory Level 2

True or False?

\quad If the integer n n can be expressed as the sum of 2 perfect squares , then 2 n 2n must also be a sum of two perfect squares.

False True

Ossama Ismail by Ossama Ismail , 63, Egypt

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1 solution

Ossama Ismail
Apr 13, 2017

Answer: True

Let n = a 2 + b 2 n = a^2 +b^2 , then 2 n = ( 2 a 2 + 2 b 2 ) = ( a + b ) 2 + ( a − b ) 2 2n = (2a^2 + 2b^2) = (a+b)^2 + (a-b)^2

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