All Questions

A. Is there natural numbers $a,b,c$ such that $\frac{a}{b+c} + \frac{b}{a+c} + \frac{c}{a+b}$ is equal to an odd natural number ? (I do not know any such numbers). B. Suppose that $\frac{a}{b+c} + \...

I have the following hyperelliptic curve of genus $2$: $$ y^2 = 561 x^6 - 41904 x^5 + 627264 x^4 + 11860992 x^3 - 197074944 x^2 + 124416^2 $$ I need to find all the rational points on this curve. ...

Given the roots $x_i$ of the depressed cubic, $$x^3+px+q=0$$ with rational coefficients. It can be shown that, in general, one can find rational $u,v$ such that, $$(u-x_1)^{1/3}+ (u-x_2)^{1/3}+ (u-...

This is inspired by a recent question about complete multipartite integral graphs. I am wondering if more can be said about tripartite integral graphs with block sizes $a<b<c$. It is easy to see ...

Now, today, my friend tell me this problem was posted by American Mathematical Monthly (Vol. 111, No. 2 Feb., 2004), p. 165 by Wu wei Chao ,and It is said that this problem is unsolved, until now. ...