Question

prove that square of any integer leave the remainder either 0 or 1 when divided by 4​

Answer 1

Answer:

Let the integer be ”x”

The square of its integer is “x²”

Let x be an even integer

x = 2q + 0

x² = 4q²

When x is an odd integer

x = 2k + 1

x² = (2k + 1)2

= 4k² + 4k + 1 = 4k (k + 1) + 1

= 4q + 1 [q = k(k + 1)]

It is divisible by 4

Hence it is proved.