The numbers in the form 3k pm 1 (k in Z) are | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The form $3k$ $(k \in Z)$ represents integers that are multiples of $3$,such as $\ldots, -9, -6, -3, 0, 3, 6, 9, 12, \ldots$.By adding $1$ or subt

Vedclass · Accepted Answer

not divisible by $3$

Vedclass · Answer

(D) The form $3k$ $(k \in Z)$ represents integers that are multiples of $3$,such as $\ldots, -9, -6, -3, 0, 3, 6, 9, 12, \ldots$.By adding $1$ or subtracting $1$ from these multiples of $3$,we obtain numbers of the form $3k + 1$ or $3k - 1$.Since $3k$ is divisible by $3$,any number of the form $3k \pm 1$ will leave a remainder of $1$ or $2$ when divided by $3$.Therefore,these numbers are not divisible by $3$.

The numbers in the form $3k \pm 1$ $(k \in Z)$ are $\ldots \ldots \ldots . .$

Similar Questions

Find the square root of $12-\sqrt{140}$.

Without actually performing the long division,find if $\frac{987}{10500}$ will have a terminating or non-terminating (repeating) decimal expansion. Give reasons for your answer.

Show that $12^{n}$ cannot end with the digit $0$ or $5$ for any natural number $n$.

Prove that the square of any odd positive integer is of the form $8m + 1$,where $m$ is a non-negative integer.

Prove that the following number is irrational: $3+2\sqrt{5}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module