SOLUTION: A finite sequence of numbers is called AWESOME if each subsequent member of the sequence, except the first one, is larger than the previous one and if the product of all the mem

Algebra ->  Permutations -> SOLUTION: A finite sequence of numbers is called AWESOME if each subsequent member of the sequence, except the first one, is larger than the previous one and if the product of all the mem      Log On


   

Question 1179548: A finite sequence of numbers is called AWESOME if each subsequent member of the sequence, except the first one, is larger than the previous one and if the
product of all the members of that sequence is a perfect square. For example, sequence 2, 6, 27 is an AWESOME sequence. Determine the natural numbers x and y such that the sequence 28, x, y, 65 is an AWESOME sequence.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


28%2Ax%2Ay%2A65+=+%282%2A2%2A7%29%2Ax%2Ay%2A%285%2A13%29

If that product is to be a perfect square, we need other prime factors of 5, 7, and 13.

5*7=35 is between 28 and 65; but that leaves us with the unused prime factor of 13.

But 13*4=52, and 52 is also between 28 and 65; and adding the additional factor of 4 keeps the product a perfect square.

ANSWER: 28, 35, 52, 65