Let be the integers a, b,c with
to be shown that the number can be written as a sum of 2 perfect squares.

(n) is the set of odd natural numbers greater than 0.

A^2 - 4b = c^2 <=> a^2 - c^2 = 4b <=> ( a + c )( a - c ) = 4b, cu a, b, c nr. intregi ;
Avem doua posibilitati :
a) a = 2x si b = 2y;
Atunci ( a + c )( a - c ) = 4b <=> x^2 - y^2 = b;
Relatia  a^2 -2b devine 2x^2 +2y^2 = ()^2 + ()^2, adica suma a doua patrate perfecte ;

b) a = 2x + 1 si b = 2y + 1 ;
In mod analog. obtii ca x^2 - y^2 + x - y = b;
si, dupa ce prelucrezi, ai ca a^2 - 2b = []^2 + []^2, adica, suma a doua patrate perfecte .

Bafta!

You need to use the logical equivalence lawsin this problem you have to use definition of implication(~p v q)i hope this