test

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Across
  1. 5. the difference between two Fibonacci numbers
  2. 6. the product of primes $p$ and $q$ such that $p+q=50$
  3. 7. a perfect fourth power
  4. 9. 15 times a prime number
  5. 11. the value of $d-b$ given $a, b, c, and d$ are positive integers satisfying $a^5=b^4$, $c^3=d^2$, and $c-a=19$.
  6. 13. a perfect square
  7. 15. gcd(768*, 17280*)
  8. 16. the largest positive integer $n$ such that $n+10|n^3+100$
  9. 17. the number of ways there are to place each of the first nine positive integers once in a $3\times 3$ grid such that no two even numbers are in adjacent tiles.
Down
  1. 1. given $f(x)=\frac{1}{2}x-2$ and $g(x)=2^x$, compute $g(f^{-1} (g^{-1}(f^{-1}(g^{-1}(1024)))))$.
  2. 2. lcm(890*, 610*)
  3. 3. a Fibonacci number plus twice the next Fibonacci number
  4. 4. a power of 2
  5. 5. a perfect cube
  6. 8. the sum of the first n positive integer powers of 3, for positive integer n
  7. 10. 2 \cdot 8192* +400
  8. 12. in regular octagon $ABCDEFGH$, $M$ is the midpoint of $\overline{EF}$ and $P$ is the intersection of $\overline{AM}$ and $\overline{BG}$. If $[ABP]=4$ and $[ABCDEFGH]=a+b\sqrt{c}$, compute abc
  9. 13. the sum of all $k^2$ such that the sum of the first $k$ odd integers divides $144$.
  10. 14. the average of 2025* and 757*