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 Cubic Equation (Posted on 2013-06-09)
Determine all triplets (a,b,c) of nonzero integers satisfying:
987654321*a + 123456789*b + c = (a + b + c)3

Prove that there are no others.

 No Solution Yet Submitted by K Sengupta No Rating

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 preliminary computer results (spoiler) | Comment 1 of 13

Let x = a + b + c

987654321*x > x^3
987654321 > x^2
x < 31427

x^3 > 987654321
x > 995

DEFDBL A-Z
FOR t = 995 TO 31427
IF t MOD 1000 = 0 THEN PRINT t;
FOR a = 1 TO t - 2
FOR b = 1 TO t - a - 1
c = t - a - b
lhs = 987654321 * a + 123456789 * b + c
sum = a + b + c
rhs = sum * sum * sum
IF lhs = rhs THEN
PRINT a; b; c, lhs
END IF
NEXT
NEXT a
NEXT t

has found so far

` a      b      c450   4500   5050  results in 1000000000000 for each side.`

It's still chugging away and has checked beyond a+b+c = 12000 so far, but not yet up to 13000.

 Posted by Charlie on 2013-06-09 15:01:35

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