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CONGRUENCE IDENTITIES INVOLVING SUMS OF ODD DIVISORS FUNCTION

. In this paper, inspired by a classical connections between partitions and divisors, we investigate some congruence identities involving sums of the odd divisor function σ odd ( n ) which is deﬁned by σ odd ( n ) = ∑ d | n d odd d . In this context, we conjectured that the congruence is valid for any positive integer n if and only if m ∈ { 2 , 3 , 6 } .