Question

证明：若N为整数,（2N+1）²-（2N-1）² 定被八整除.

Answer 1

(2N+1)^2-(2N-1)^2

=[(2N+1)+(2N-1)][(2N+1)-(2N-1)]

=4N*2

=8N

所以能被8整除

5x^2-3y^2

=(√5x)^2-(√3y)^2

=(√5x+√3y)(√5x-√3y)

a^2+b^2-c^2+2ab-2bc-2ca

=(a^2+2ab+b^2)-2bc-2ca+c^2

=(a+b)^2-2c(a+b)+c^2

=(a+b-c)^2

=(k+3+2k+2-3k+1)^2

=6^2

=36