Abstract
A number of linear congruences modulo r are proved for the number of partitions that are p-cores where p is prime, 5 ⩽ p ⩽ 23, and r is any prime divisor of ½(p − 1). Analogous results are derived for the number of irreducible p-modular representations of the symmetric group Sn. The congruences are proved using the theory of modular forms.
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