goformit100
  • goformit100
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.
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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 :)
goformit100
  • goformit100
Ok
anonymous
  • anonymous
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 :)

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goformit100
  • goformit100
Thankyou
anonymous
  • anonymous
You're welcome! :)

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