Show that any positive integer when squared leaves remainder 0 or 1 on division by 4.
What is the remainder when the square of an odd integer is divided by 4?

Question

Show that any positive integer when squared leaves remainder 0 or 1 on division by 4. What is the remainder when the square of an odd integer is divided by 4?

Accepted Answer

1. An odd integer is 2k+1; its square is 4k^2 + 4k + 1 = 4(k^2+k) + 1, so the remainder is 1.

Show that any positive integer when squared leaves remainder 0 or 1 on division by 4.
What is the remainder when the square of an odd integer is divided by 4?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Euclid's Division Lemma practice

Show that any positive integer when squared leaves remainder 0 or 1 on division by 4.What is the remainder when the square of an odd integer is divided by 4?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Euclid's Division Lemma practice

Show that any positive integer when squared leaves remainder 0 or 1 on division by 4.
What is the remainder when the square of an odd integer is divided by 4?