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April 18th, 2019, 12:43 AM  #1 
Newbie Joined: Apr 2019 From: Europe Posts: 1 Thanks: 0  Expression for finding common elements in two series
Hello, 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.? 
April 19th, 2019, 11:58 AM  #2 
Senior Member Joined: Dec 2015 From: somewhere Posts: 510 Thanks: 79 
Without equating them then use divisibility rule. $\displaystyle kx(x+1)$ or S1 is divisible by k. S1(mod)k=0 .To continue use modular arithmetics. 

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common, elements, expression, finding, number theory, sequence and series, series 
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