m² – 1 is divisible by 8, if m is (a) an even integer
(b) an odd integer
(c) a natural number
(d a whole number
Answers
Answer:
an odd number is the correct answer to this question .
Given : m² – 1 is divisible by 8
To Find : m is:
(a) an even integer
(b) an odd integer
(c) a natural number
(d a whole number
Solution:
m² – 1 is divisible by 8
take m = 2
which is even integer , natural number , whole number
2² - 1 = 4 - 1 = 3 is not divisible by 8
Hence only option left is
odd integer
now odd integer can be represented as 2k + 1
m² - 1
= (2k + 1)² - 1
= 4k² + 4k + 1 - 1
= 4k(k + 1)
in k , k+1 one must be even number
Hence 4k(k + 1) is divisible by 8
so m² – 1 is divisible by 8 if m is an odd integer
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