The partition is $p$-regular precisely when
$$
a_j<p\qquad\text{for every }j,
$$
that is, when no part occurs $p$ or more times. This is the definition of a <regular partition> in <characteristic of a field> $p$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 160 / 4 / c / i / Solution

 Solution

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