If m and n are positive integers and (m-n) is | vedclass

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

Question

(A) We know that $m^{2}-n^{2} = (m-n)(m+n)$.Given that $(m-n)$ is an even number,let $(m-n) = 2k$ for some integer $k$.Since $(m+n) = (m-n) + 2n$,and

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) We know that $m^{2}-n^{2} = (m-n)(m+n)$.Given that $(m-n)$ is an even number,let $(m-n) = 2k$ for some integer $k$.Since $(m+n) = (m-n) + 2n$,and $(m-n)$ is even,$(m+n)$ must also be an even number because the sum of two even numbers is even.Let $(m+n) = 2j$ for some integer $j$.Therefore,$(m^{2}-n^{2}) = (2k)(2j) = 4kj$.This shows that $(m^{2}-n^{2})$ is always divisible by $4$.

If $m$ and $n$ are positive integers and $(m-n)$ is an even number,then $(m^{2}-n^{2})$ will be always divisible by

Similar Questions

$A$ number when divided by $44$, gives $432$ as quotient and $0$ as remainder. What will be the remainder when dividing the same number by $31$?

In a Mathematics examination,the marks scored by $5$ candidates are $5$ successive odd integers. If their total marks are $185,$ the highest score is

The difference between the squares of two consecutive numbers is $35.$ The numbers are

If the sum and difference of two numbers are $20$ and $8$ respectively,then the difference of their squares is

$46818 + 34484 - 24642 - 21232 = ?$

Vedclass Test Series

Exam Paper Generator

Online Exam Module