Sums of Squares
The current Macalaster Problem of the Week (#841) reads:
Find the first integer k for which 169 is not the sum of k nonzero squares.
The squares are not necessarily unique. For example 169=1+4+4+16+144.
Here are some extensions I think are also worth investigating:
The Macalaster problem suggests that behind the decompositions is the
request for an efficient computer algorithm. If you find a good one,
please send it along.
- The above problem.
- For each k from 1 to 10 (and farther?), find the first integer
which is the sum of 1,2,...,k nonzero squares.
- Find the integer from 1 to 100 which can be decomposed into sums of
1,2,...,k nonzero squares, where k is a maximum.
- Find the integer from 1 to 100 which can be decomposed into the
most different sums of squares (not necessarily 1,2,...,k).
Macalester College Problems of the Week
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