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Cubic coefficients (Posted on 2020-11-02) Difficulty: 2 of 5
The coefficients a,b,c of a polynomial f:R->R, f(x)=x3+ax2+bx+c are mutually distinct integers and different from zero. Furthermore, f(a)=a3 and f(b)=b3. Determine a,b and c.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Possible solution; rest of a solution Comment 3 of 3 |
(In reply to re: Possible solution; rest of a solution by Brian Smith)

Well done, Brian Smith!

Here's a program (unnecessary since it's been proved) which shows the same result for (a,b,c) = (-2,4,16)

def f(x,a,b,c):
    return x**3 + a*x**2 + b*x + c

bigNum = 100
for a in range(-bigNum, bigNum+1):
    if a == 0:
        continue
    for b in range(-bigNum, bigNum+1):
        if b == a or b == 0:
            continue
        for c in range(-bigNum, bigNum+1):
            if c == b or c == a or c == 0:
                continue
            if f(a,a,b,c) != a**3 or f(b,a,b,c) != b**3:
                continue
            print(a,b,c)

  Posted by Larry on 2020-11-08 08:24:56
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