Let a,b,c,d and e be in the A.P such that a+b+c+d+e is the cube of an integer and b+c+d is square of an integer. Then the least possible value of c is

If m,n,o are in AP then m+o = 2n
so sum of m,n,o = m+n+o = 2n+n = 3n
so basically 3 times the middle number
same concept will be used for 4 AP numbers or 5 AP numbers ,etc

So number c= 675

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