There are two related questions this month:
1 | = | 1^{2} |
2 | = | -1^{2} - 2^{2} - 3^{2} + 4^{2} |
3 | = | -1^{2} + 2^{2} |
4 | = | -1^{2} - 2^{2} + 3^{2} |
5 | = | 1^{2} + 2^{2}. |
Can every positive integer n be written as a_{1} 1^{2} + a_{2} 2^{2} + ... a_{k} k^{2}, where a_{i} = ±1?
Source: Loren Larson