Question

The remainder when the square of any prime number greater than 3 is divided by 6, is:

Answer 1

Step-by-step explanation:

Square of any prime number greater than 3

= (6n±1)² , where n€N

= (6n)²±2×6n×1+1²

/* From an algebraic identity:

(a±b)² = a²±2ab+b² */

= 36n²±12n+1

= 6(6n²±2)+1

= 6m +1 /* Here , m = 6n²±2

Therefore,.

Remainder = 1

/* By Euclid's Division Lemma

Or

Square of prime numbers greater than 3 are

5²=25 = 6×4+1

7² =49= 6×8+1

11² =121 = 6×20+1

13² = 169 = 6×28+1

By Euclid's Division Lemma,

Remainder = 1