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Congruences involving<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$F$"><mml:mi>F</mml:mi></mml:math>-partition functions
The primary goal of this note is to prove the congruence Ļ 3 (3 n + 2) ā” 0(mod3), where Ļ 3 ( n ) denotes the number of F āpartitions of n with at most 3 repetitions. Secondarily, we conjecture a new family of congruences involving c Ļ 2 ā¦