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Thu, 31 Jan 2008
Ramanujan's congruences
Ramanujan's congruences state that:
Looking at this, anyone could conjecture that p(13k+7) = 0 (mod 13), but it isn't so; p(7) = 15 and p(20) = 48·13+3. But there are other such congruences. For example, according to Partition Congruences and the Andrews-Garvan-Dyson Crank:
$$ p(17\cdot41^4k + 1122838) = 0 \pmod{17} $$ Isn't mathematics awesome?
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