Question

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

Answer 1

Answer:

Answer Expert Verified

Every integer when squared leaves a the remainder 0 or 1 when divided by 4. So, every even integer squared leaves a remainder 0 when divided by 4. And every odd integer squared leaves a remainder 1 when divided by 4. Hence, any integer squared leaves a reminder 0 or 1 when divided by 4.

Answer 2

Answer:

1st way

Every integer when squared leaves a the remainder 0 or 1 when divided by 4. So, every even integer squared leaves a remainder 0 when divided by 4. And every odd integer squared leaves a remainder 1 when divided by 4. Hence, any integer squared leaves a reminder 0 or 1 when divided by 4.

2nd way

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

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