Question

2. What is the remainder you get on dividing 13²³ + 1 by 12?​

Answer 1

Remainder would be 2 if we divide 13²³ + 1 by 2.

We have to find the remainder we get on dividing 13²³ + 1 by 12.

Concept :

• In mathematics, Remainder is the integer ‘left over’ after dividing one number by another number to get an integer quotient.
• When a number a , is divided by b getting q as quotient and r as remainder then, a = bq + r , where 0 ≤ r < b
• If a number (ax + b)ⁿ is divided by a , where a > b then remainder would be (b)ⁿ.

Using above concept,

we have to divide 13²³ + 1 by 12.

let's arrange 13²³ + 1 in such a way that it contains 12.

∴ 13²³ + 1 = (12 × 1 + 1)2²³ + 1

now We divided [(12 × 1 + 1)²³ + 1] by 12.

so remainder = Rem [(12 × 1 + 1)²³/12] + Rem [1/12]

= 1²³ + 1

= 1 + 1

= 2

Therefore the remainder would be 2.