# Tagged Questions

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### How can I solve equation $x^2 - y^2 -2xy - x + y = 0$?

I have this equation with 2 variables - $$x^2 - y^2 -2xy - x + y = 0$$ The only condition I have is that $x + y$ should be greater than $10^{12}$. EDIT - I need $x$ and $y$ to be integer. I ...
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### About a Variant of Ulam Spiral

Here I read about a variant on the Ulam spiral: [A] structure may be seen when composite numbers are also included in the Ulam spiral. [...] Using the size of the dot representing an integer ...
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### Integral values of an expression

Let $b=\sqrt{a^2+5a+8}-\sqrt{a^2-3a+4}$ Find number of integral values of b. My $long$ way using Calculus : Find domain of function : $R$ Note that function is continuous Prove the function is ...
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### is there an analytic solution to $n^2+kn-d=m^2$ m,n integers

For $k=24,d=-17;m=8,n=3$, completing the square gives $(12+n)^2=m^2+161$ Where $161$ just happens to be the product of two primes $(q=7,p=23)$, so for large $k,m,n$ factoring may be very slow. ...
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### Difference between fields $\mathbb{Q}[\sqrt{2}+\sqrt{3}]$ and $\mathbb{Q}[\sqrt{2},\sqrt{3}]$? [duplicate]

Possible Duplicate: Is $\mathbf{Q}(\sqrt{2}, \sqrt{3}) = \mathbf{Q}(\sqrt{2}+\sqrt{3})$? How would one describe elements from $\mathbb{Q}[\sqrt{2}+\sqrt{3}]$ and ...