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Question

If 'a', 'b', 'c' and 'd' are consecutive natural numbers and a3=b3+c3+d3, what is the least value of 'a'?

A
6
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B
9
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C
3
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D
12
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Solution

The correct option is A 6
a3=b3+c3+d3 is possible for consecutive natural numbers only if a>b>c>d
Therefore, b=(a1),c=(a2),d=(a3)
a3=(a1)3+(a2)3+(a3)3
a cannot be 3 as this will make d=0 and it is given in the question that all a,b,c,d are natural numbers
Substituting for a from the answer option, starting with the least number
If a=6, then LHS=a3=33=216, and
RHS= (a1)3+(a2)3+(a3)3 =53+43+33=125+64+27=216
We can see LHS=RHS
We can stop here as we want the least value for a.
Hence, 6 is the correct answer.

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