Thursday 24 December 2015

Completing a sequence

Here are six numbers in sequence.You have to find the next 2 numbers-
202    122   232   425  262  728

Monday 7 December 2015

Pell equations

An equation of the type p^2-Nq^2=1 has been classified as Pell equation though it did not evolve from Mr Pell.
Given any value of N,one can find the values of p and q which satisfy this equation.
I have done extensive research on the subject ,finding the values of p and q for very many values of N-almost all upto 99 and some more values above 100.
There is a method for finding the solutions and this was used by me.
For values of N just above or below a perfect square the procedure does not require many steps but for values like 53,73 of N more steps were needed
As a variation for some values of N,you can get a solution for the alternative equation p^2-Nq^2=(-)1 after a few steps but will need more steps for p^2-Nq^2=1.
Examples -
N=24-solution p=5 q=1,more solutions can be found later like p=49,q=10
N=26......p=51q=10...p=5201,q=1020
N=48....p=7,q=1....p=97,q=14
N=50...p=99,q=14
N=53...p=66249,q=9100...This  number N has solution p=182 q=25 for the alternative equation involving the final result as (-)1