# Zsbán Ambrus

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 Mar8 comment What was the first bit of mathematics that made you realize that math is beautiful? (For children's book) I think it's more impressive that if you subtract one from that number, you get its reciprocial. May15 comment Monochromatic triangles in a two-coloring of the plane This is posed as a difficult problem number 14.8 in Lovász László, Combinatorial Problems and Exercises, 2nd ed. You may check out the hints given there in the hints section. Mar11 comment Number of integer solutions to $3i^2 + 2j^2 = 77 \cdot 6^{2012}$ I don't understand. So what if the ratio $i/j$ is neither 5 nor 5/3? Mar9 comment What makes elementary functions elementary? That definition sounds wrong to me. By that definition, $\sin x = ax + b$ would have an elementary solution $x$ as a function of $a, b$. Mar4 comment Need some help settling a bet Also, in the future, please try to use titles for your posts that help people browsing the titles to decide whether they might be able to help in your question. Eg. here you could use the title “Is there a power of two divisible by three?” or “Splitting pizza to three people evenly by repeatedly halving slices”. Mar4 comment Puzzle: $(\Box @)+(\Box @) = (\Box\bigstar\Box$) @barf: it was probably downvoted because there's an earlier answer that seems complete enough. Mar4 comment How many fours are needed to represent numbers up to $N$? By the way, if you allow logarithms, you don't even need four fours: actually three fours are enough to represent any positive integer like $\log\bigl(\log 4/\log(\surd\surd\dots\surd4)\bigr)/\log 4$.