Binomial Theorem And Its Simple Applications Question 64
Question: If m, n are any two odd positive integers with $ n<m $ , then the largest positive integer which divides all the numbers of the type $ m^{2}-n^{2} $ is
Options:
A) 4
B) 6
C) 8
D) 9
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] Let $ m=2k+1,,n=2k-1(k\in N) $
$ \therefore m^{2}-n^{2}=4k^{2}+1+4k-4k^{2}+4k-1=8k $
Hence, all the numbers of the form $ m^{2}-n^{2} $ are always divisible by 8.
BETA
