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