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.

(In reply to an open letter to Charlie by Ady TZIDON)

I will see how long the following takes:

DEFDBL A-Z
FOR t = 995 TO 31427
    IF t MOD 1000 = 0 THEN PRINT t;
    term1 = 0
    FOR a = 1 TO t - 2
        term1 = term1 + 987654321
        term2 = 0
        FOR b = 1 TO t - a - 1
            term2 = term2 + 123456789
            c = t - a - b
            lhs = term1 + term2 + c
            rhs = t * t * t
            IF lhs = rhs THEN
                PRINT
                PRINT a; b; c, lhs
            END IF
        NEXT
    NEXT a
NEXT t

Notice also I eliminated the redundant sum, when t already had that sum.

Posted by Charlie on 2013-06-10 21:35:38