PROOF OF A CONGRUENCE FOR HARMONIC NUMBERS CONJECTURED BY Z.-W. SUN
نویسندگان
چکیده
منابع مشابه
Proof of two Divisibility Properties of Binomial Coefficients Conjectured by Z.-W. Sun
For all positive integers n, we prove the following divisibility properties: (2n + 3) ( 2n n ) ∣∣∣∣3(6n 3n )( 3n n ) and (10n + 3) ( 3n n ) ∣∣∣∣21(15n 5n )( 5n n ) . This confirms two recent conjectures of Z.-W. Sun. Some similar divisibility properties are given. Moreover, we show that, for all positive integers m and n, the product am ( am+bm−1 am )( an+bn an ) is divisible by m + n. In fact,...
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2012
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042112500649