A double angle formula: $sin 2x = 2 sin x cos x$.

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A $5 by 8$ chessboard contains $5 times 8 = 40$ little squares.

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$f(x+h) + g (y+k)$

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We have $abs u+v <= abs u + abs v$ for all $u,v in CC$,
while $norm(vec u + vec v)^2 = norm(vec u)^2 + norm(vec v)^2$ only if $vec u perp vec v$.

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$Gamma(s) = \int_0^infty e^-x x^s dx/x$ and
$$
int log x dx = x log x - x + C
$$

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If $A$ is a permutation matrix then $abs(det A) = 1$

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If $g \in G$ then $order g | order G$

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If $a$ and $b$ are finite sets, then $card(a product b) = card a times card b$

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If $a x^2 + b x + c = 0$ then $x = (-b pm sqrt(b^2 - 4 a c))/2a$,
and
$$"if" a x^2 + b x + c = 0 "then" x = (-b pm sqrt(b^2 - 4 a c))/2a
$$

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$$zeta(s) = \sum_n=1^infty 1/n^s = prod_p (1-p^-s)^-1$$


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$$
abs x = cases:
    x if x > 0
    0 if x = 0
    -x otherwise
$$
Another line.

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$$
derivation:
int_A^T 1/(x log x llog x) dx = lllog T + bigO(1)

asymp lllog T
$$
as $T to infty$.

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$$
system:
   a + b = c < 8
      +55

   a^2 <= 77 b^3 + 12

   x^n + y^n = z^n
$$