Congruence Properties modulo 5 and 7 for the Pod Function
نویسنده
چکیده
In this paper, we prove arithmetic properties modulo 5 and 7 satisfied by the function pod(n) which denotes the number of partitions of n wherein odd parts must be distinct (and even parts are unrestricted). In particular, we prove the following: For all n ≥ 0, pod(135n + 8) ≡ 0 (mod 5), pod(135n + 107) ≡ 0 (mod 5), pod(135n + 116) ≡ 0 (mod 5), pod(675n + 647) ≡ 0 (mod 25), pod(3375n + 1997) ≡ 0 (mod 125), pod(3375n + 3347) ≡ 0 (mod 125), pod(567n + 260) ≡ 0 (mod 7), and pod(567n + 449) ≡ 0 (mod 7).
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