Recent content by sparsh12

--> 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...

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--> 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' ?

Why no reply yet?

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...

I have changed the question,under the title: Travelling Salesman Problem, in number theory page.

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...