Find all possible solutions:
P=(x-1)*(x-2)*(x-4)*(x-8) =ax^2
Solve to get (x,y) for P(a)
Evaluate:
i. (x,y) for a=7 (original version)
ii. for a=4 (more friendly results!)
Credit: Valery Volkov
(In reply to
re: answer by Brian Smith)
I have read your remarks re Y y ...and I truly appreciate your
analysis.
Personally I see a very little difference between "ugly" and mundane numbers.
I have also read your solution and found it normal and direct,
As to non-common approach , paying attention that 2*4=1*8
one might continue:
(x^2-9x+8)*(x^2-6x+8) =ax^2
and then continue with z=x^2+8
)You may try it and see that it is simpler that way or just trust me.
Anyway the general solution is preferable since at the time of those olympiads the appropriate software was either non-existant or not admissible.
Thank you for your post.
Edited on April 28, 2023, 4:11 am
re(2): answer
