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RE: Brainsteem Mathematics Challenges: Divisibility by 65
How do we then know it works for all n?
Just the idea! The algebra can be long.
How do we then know it works for all n?
Just the idea! The algebra can be long.
It's easy)))
f(1) divided by 65
let f (n) is divided by 65
divide by 65 this f(n+1)-f(n)
f(n+1)-f(n)=65n12+390n11+1430n10+3575n9+6435n8+8580n7+8580n6+6435n5+3575n4+1430n3+390n2+65n+65n4+130n3+130n2+65n+585
all coefficients are divided by 65
therefore, the f(n) is divided into 65 for all n