Grade 1010 grade maths
Prove that if x & y are odd positive integers then x^2+y^2 is even but not divisible by 4
1 Answer
S. Haris Ahmed Irfan
all odd positive integers are of form 2q+1
therefore let x=2q+1 and y=2p+1 (where p and q are integers)
x^2=(2q+1)^2=4q^2+1+4q
y^2=(2p+1)^2=4p^2+1+4p
therefore x^2+y^2=4q^2+1+4q+4q^2+1+4q
after rearranging
4(q^2+p^2+p+q)+2
this number is clearly even but is not divisible by 4 {since 2 is added at the end}
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