how can i prove that n is even n2 is even let n be an even

how can i prove that n is even -> n² is even

let n be an even integer

n = 2k

n² = ( 2k²)

.... and then please complate this and explain step by step

thanks

Solution

Answer:

Let n be an even integer

n = 2k ----> give any value to k , it will be always an even number in the result

n^2 = ( 2k^2) -----> put value n = 2 here we get 2k^2 is also an even

(2k)^2=4k^2=2(2k^2)=2k\' , hence proved

By using induction we proved it. There is nothing logical in it.