(m+1)2 = 24n+ 2m +2. m is less than 100 and n is any whole number. Find the number of possible values of m ?
Options:
A . 10
B . 32
C . 18
D . none of these
E . π
Answer: Option D : D Option (d) m2 -1 =24n. This means that when m2 is divided by 24 it leaves a remainder -1. m is of the form (6p+1)2 or (6p-1)2.. This is equal 12p(3p+/-1)+1.. We can see that the term 12p(3p+/-1) Is always divisible by 24..,Therefore we have to find the possible values of (6p+1) and ( 6p-1) less than 100. Answer is 33..
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