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 Yearling
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Oct
9
awarded  Yearling
Dec
6
answered Prove that $e^x\ge x+1$ for all real $x$
Dec
1
comment Integer solutions to $\sqrt{a} + \sqrt{b} = \sqrt{c}$
Obviously this is overkill, I included it because the same method allows you to write down all pythagorean triples or all (a^2, b^2, c^2) in arithmetic progression.
Dec
1
answered Integer solutions to $\sqrt{a} + \sqrt{b} = \sqrt{c}$
Nov
27
awarded  Teacher
Nov
27
comment Are there infinitely many pairs of rational numbers such that…
I chose 7 because this was the smallest square-free positive integer for which both curves have positive rank. If you don't care that $a$ and $b$ vary, you could take $b=0$ and look at the curve $2r^2=a^3+1$, which has infinitely many rational points.
Nov
27
answered Are there infinitely many pairs of rational numbers such that…