--> if n = x(mod 10x+1) n,x>0 (where = is symbol used in "congruence" not equality)
then, is there a way to find some direct relation between n and x, in terms of some parameter?
--> I have 9 more such equations and if i am able to solve either one i would be able to solve all of...
--> Yeah i have heard of Chinese remainder theorem but i have never dealt with linear systems of congruence equations.
--> And i observed that both congruences are actually equivalent, so i feel the problem doesnot remain a system of congruence equation, as i infer from it's...
if,
10x+1 divides n-x
and 10x +1 divides 10n +1 , where x is a variable and positive integer while n is a constant and positive integer.
then, is there a way to find, of what form x must be, in terms of 'n' ?
I change the question completely. If i get an answer for this, my question would be resolved.
Everyone is obsessive of finding minimum distance in Travelling Salesman Problem, but my question is,
"Is there a way to find the maximum distance possible?"
I know it is related to theory of...
if {x1 , x2 , ...xi} and {y1,y2,...yi} are finite sets.
are two sets of real numbers. Then sum
Ʃ xixj +yiyj must be maximum, and i≠j
so is there some general condition to solve this problem?
A quadratic diophantine equation is of form:
Ax^2 + Bxy + Cy^2 +Dx + Ey + F =0
Now, for A=0 and C=0,
Bxy + Dx + Ey + F=0 ...(1)
moreover there is one more condition, gcd(B,D,E)=1
So how do I find if some integral solution of (1) exists or not?
I am not interested in the solution...
i am interested in Riemann zeta function. i am in a high school.
i have good hold over calculus(at least what's required for physics).
Would Tom Apostle's Calculus I be good to further improve my skills.
What should i do next?
Real Analysis or Complex Analysis or directly analytic number...
i just read somwhere that
if cos a = cos d
then a=2n(pi)±d where n is integer
So, if cos (b*ln (i/j))= cos (-b (lni/j))=cos(b*ln(j/i))
can i write
b*ln i/j = 2n(pi)±b*ln(j/i)
or
bln(j/i)+bln(i/j)=2n(pi) or 2n(pi)=0
b=n(pi)/(ln(i/j)-ln(j/i))=n(pi)/(b*ln(i/j))
then replace b in...
I don't know anything of complex analysis or analytic number theory or analytic continuation. But i read about zeta function and riemann hypothesis over wikipedia, clay institute's website and few other sources. I started with original zeta function...