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COMMENTS
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The seven pairs are [6,8], [8,12], [12,24], [15,40], [16,48], [20,120], [21,168]. The list is definite, but the conjecture is unproved. The conjecture asserts that
"Sum_{ak+1 square} p(n-k) == 1 mod 2 if and only if bn+1 is a square" holds if and only if [a,b] is one of these seven pairs.
Here p(n) is the number of partitions of n, A000041.
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