Principle Of Mathematical Induction Question 29
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
Correct Answer: C Let $ m=2k+1,,n=2k-1\ (k\in \mathbb{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.
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Answer:
Solution:
BETA
