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 smallest possible value of c.

Answer 1

Ahh, this question :) Shall I give it a try too? Since I was warned by a kind moderator, I shall attempt to guide you through :)

Substitute a, b, c, d and e for n-2, n-1, n, n+1 and n+2. We then see that the sum, 3n, is a perfect square and the sum, 5n, is a perfect cube.

There you go! A great hint to solving the question! Hope this helped, have a great day :)

Answer 2

Ok

Answer 3

Okay maybe that wasn't that helpful. What if we actually equate them to the numbers? We get 3n as a square. So we know n must have a factor 3 in it. Then let's take a look at 5n. It is a cube, implying that n must have 25 in it. Hope this helped :)

Answer 4

Thankyou

Answer 5

You're welcome! :)