20190615, 11:45  #1 
"Vasiliy"
Apr 2017
Ukraine
63_{10} Posts 
Searching many formulas to one limit
Hi guys!
This is formula for nth rgonal pyramidal number I have , for example 2<r<1000. And i want to search all this numbers to one constant border(for example 10^{15}) How i can find such n's in C++? Prethanks 
20190616, 08:43  #2 
"Vasiliy"
Apr 2017
Ukraine
3^{2}·7 Posts 
And i forget about searching from some minimal border.
How to find n_{min} without computing previous ? Prethx 
20190624, 15:12  #3 
Oct 2007
Manchester, UK
552_{16} Posts 
What exactly are you searching for?

20190625, 06:34  #4 
"Vasiliy"
Apr 2017
Ukraine
111111_{2} Posts 
Im searching for numbers that ngonal pyramidal number and nangular number. Cannonball problem for different bases

20190625, 16:37  #5  
Feb 2017
Nowhere
11614_{8} Posts 
Quote:
Multiplying by 1/2*(r  2) and adding 1/16*r^2  1/2*r + 1 gives a square y^2. (Note that when r = 4 you multiply by 1 and add 0). Thus, for a given r you can write where the P is the n^{th} rpyramidal number, which is cubic in n. For any given r, this is an elliptic curve. This gives a mighty bludgeon to use on the problem. For r = 4, there are elementary proofs that n = 70 is the only n > 1 giving a square value for the cannonball problem. Last fiddled with by Dr Sardonicus on 20190625 at 16:39 Reason: xingif posty 

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