Some New q-Congruences for Truncated Basic Hypergeometric Series: Even Powers
نویسندگان
چکیده
منابع مشابه
Some New Super-congruences modulo Prime Powers
Let p > 3 be a prime. We show that p−1 k=0 −1/(p + 1) k p+1 ≡ 0 (mod p 5) and p−1 k=0 1/(p − 1) k p−1 ≡ 0 (mod p 4). For any positive integer m ≡ 0 (mod p), we prove that p−1 k=0 (−1) km p/m − 1 k m ≡ 0 (mod p 4), and p−1 k=1 (−1) km k 2 p/m − 1 k m ≡ 1 p p−1 k=1 1 k (mod p 3) if p > 5. The paper also contains some open conjectures.
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ژورنال
عنوان ژورنال: Results in Mathematics
سال: 2019
ISSN: 1422-6383,1420-9012
DOI: 10.1007/s00025-019-1126-4