We define a factoriangular number (Ftn) as the sum of a factorial and its corresponding triangular number, that is, Ftn = n! + n(n+1) / 2. If both n and m are natural numbers greater than or equal to 4, is there an Ftn that is a divisor of Ftm? Please also see the article provided in the link below, specifically Conjecture 2 on pp. 8-9.
Article On the Sum of Corresponding Factorials and Triangular Number...
Ioulia N. Baoulina
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Let m=Ftn if Ftn is odd, and m=2Ftn if Ftn is even. Then Ftn divides Ftm.
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Ioulia N. Baoulina
Let m=Ftn if Ftn is odd, and m=2Ftn if Ftn is even. Then Ftn divides Ftm.
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Evgeniy Martyushev
Dear Romer, there are a lot of counter-examples, even if we eliminate the pairs proposed by Ioulia. For instance, m=51, n=4 or m=38, n=6, etc.
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