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April 18th, 2019, 12:43 AM   #1
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Expression for finding common elements in two series

First of, I am sorry if I am posting it in a wrong section. If so, can someone please move this thread to the appropriate section?

Now, my problem:
I have a series of the form S1=x(x+1)
and another series S1/k, for any k∈N. Now I want to find the values where the elements of two series are equal. For example, let k be 3, then the intersection of the two series gives 2,30,420,5852,81510,1135290. Can a formula be derived to find these ways without resorting to equating the two series and deriving quadratic roots i.e. using series formulae or triangular numbers etc.?
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April 19th, 2019, 11:58 AM   #2
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Without equating them then use divisibility rule.
$\displaystyle k|x(x+1)$ or S1 is divisible by k.
S1(mod)k=0 .To continue use modular arithmetics.
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