This title space is too small! The topic is Hardy-Ramanujan numbers.

Computer Science Level 3

This problem's question: 6963472309248 is first sum of paired cubes that can be done four different ways. What is the sum of the positive integers that comprise those four pairs (eight positive integers altogether)?

See A011541 .

This is not a pencil-and-paper problem. It does take a small number of seconds on a 4.5GHz computer to find the pairs, which are not in the link mentioned above.

The answer is 104112.

1 solution

A Former Brilliant Member
Jun 16, 2019

The upper limit on the positive integers to be checked: $19096$

The four pairs, which when cubed sum to 6963472309248:

$\begin{array}{cc} 2421 & 19083 \\ 5436 & 18948 \\ 10200 & 18072 \\ 13322 & 16630 \\ \end{array}$

The sum of the positive integers that comprise the pairs: $104112$

s = 6963472309248;
q = Timing[n = Ceiling[N[Power[s, (3)^-1]]];
   Print[n];
   c = Table[i^3, {i, n}];
   ParallelTable[j = Power[s - i^3, (3)^-1]; 
    If[j \[Element] Integers \[And] i <= j, {i, j}, Nothing], {i, n}]
   ];
Print[q];
Print[Plus @@ Flatten[q[[2]]]]

This title space is too small! The topic is Hardy-Ramanujan numbers.

The answer is 104112.

1 solution

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