Let a,b,c,d,e be consecutive positive integers ,s

Question

Let a,b,c,d,e be consecutive positive integers ,such that, (b+c+d) is a perfect square and (a+b+c+d+e) is a perfect cube. Find the smallest value of c.

Venkat · Accepted Answer

Since the middle term of an arithmetic progression with an odd number of terms is the average of the series, we know and . Thus, must be in the form of based upon the first part and in the form of based upon the second part, with and denoting an integers. is minimized if it’s prime factorization contains only , and since there is a cubed term in , must be a factor of . , which works as the solution.

Algebra> Let a,b,c,d,e be consecutive positive int...

Let a,b,c,d,e be consecutive positive integers ,such that, (b+c+d) is a perfect square and (a+b+c+d+e) is a perfect cube. Find the smallest value of c.

cSGhj , 7 Years ago

Venkat

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Algebra> Let a,b,c,d,e be consecutive positive int...

Let a,b,c,d,e be consecutive positive integers ,such that, (b+c+d) is a perfect square and (a+b+c+d+e) is a perfect cube. Find the smallest value of c.

cSGhj , 7 Years ago

Venkat

LIVE ONLINE CLASSES

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