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KVPY2013MathematicsSequences and Series

Let a, b, c, d, e be natural numbers in an arithmetic progression such that a+b+c+d+e is the cube of an integer and b + c + d is square of an integer. The least possible value of the number of digits of c is

Options

  1. A2
  2. B3
  3. C4
  4. D5

Correct answer

B. 3

Step-by-step solution

a=C-2 Db=C-Dc=Cd=C+De=C+2 Da+b+c+d+e=5 c= ³b+c+d=3 c= ² 3 ³=5 ² ³ 5 = ² 3 least possibility =5 3, =5 3 3 =15 =45C= (45)² 3 =15 45=675

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