Research articles
ScienceAsia 51 (2025):ID 2025052 1-7 |doi:
10.2306/scienceasia1513-1874.2025.052
Anote on the congruences with sums of powers of trinomial coefficients
Zhongyan Shen*, Lixia Ye
ABSTRACT: Trinomialcoefficients n
k 2
aredefinedby
(1+x+x2)n=
2n
k=0
n
k 2
xk.
Letp>3beaprimenumberandn,mbepositiveintegers,weobtainedthecongruencesmodulop2withpartialsums
ofpowersoftrinomialcoefficients
0?3k+i?p?1
np?1
3k+i
m
2
and
0?3k+i?p?1
2
np?1
3k+i
m
2
(0?i?2).
Wealsostudiedthecongruencesmodulop2withsumsofpowersoftrinomialcoefficients
p?1
k=0
np?1
k
m
2
and
p?1
2
k=0
np?1
k
m
2
.
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Department of Mathematics, Zhejiang International Studies University, Hangzhou 310023 China |
* Corresponding author, E-mail: huanchenszyan@163.com
Received 18 Aug 2023, Accepted 9 Jun 2025
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